JP2004045231A - Coordinate measuring machine, method for calibrating the coordinate measuring machine, and computer-readable storage medium storing a program for executing the method - Google Patents

Abstract

An object of the present invention is to provide a three-dimensional measuring machine, a method of calibrating a three-dimensional measuring machine, which can determine three squareness errors from which a probe error is separated, and can further simplify an arithmetic process for obtaining the squareness error. It is an object of the present invention to provide a computer-readable storage medium storing a program for executing the method.
According to the method of calibrating a coordinate measuring machine having a probe for detecting the position of a surface to be measured in a Z direction according to the present invention, the N surface having a known true surface shape and similar shapes to each other is used. The method is characterized in that the shapes of N (N is a positive integer) reference measurement objects are measured, and three squareness errors of a three-dimensional orthogonal coordinate axis are detected based on the measured shape data of the N reference measurement objects. There is.
[Selection diagram] Fig. 4

Description

（１）
【０００７】
ただし、（ｉｓ、ｊｓ、ｋｓ）はｓ方向の単位ベクトルを示し、Ｑは理想的な直交座標系から現実の座標系への座標変換行列である。このとき、理想の座標系における、原点から距離Ｒの点Ｐの集合、すなわち半径Ｒの球面は、現実の座標系（Ｘ、Ｙ、Ｚ）においては、下記の（２）式の内積で表される曲面となる。
【０００８】
【数２】

【０００９】
この（２）式を陽関数で表すと、α＜＜１、β＜＜１、γ＜＜１を考慮して下記の（２’）式を得る。
【００１０】
【数３】

（２’）
【００１１】
この（２’）式は、（１）式の座標変換行列Ｑによって、理想の座標系における球面が、現実の座標系では楕円面に写像されることを表している。つまり、測定座標系の直角度が狂っていると、球面が楕円面として測定されてしまう。したがって、実際の三次元測定機の運用では、予め行う校正によってα、β、γを求めておき、現実の座標系で測定される座標（ｐＸ、ｐＹ、ｐＺ）に対して、逆変換Ｑ^−１を行うことで測定データを補正する。
【００１２】
このようなプローブを用いた形状測定法では、上記直角度誤差の他にもプローブ誤差が発生する。このプローブ誤差が、所望の測定精度に対して無視できない場合には、補正が必要となるので、プローブ誤差を測定する必要がある。ここでいうプローブ誤差とは、プローブが原因で発生する、被測定面の法線方向に依存した系統誤差を指す。具体的には、接触式プローブの場合であればプローブ先端球の真球度誤差、光学式変位計を被接触プローブとして用いる場合であれば、光学式変位計の光軸に対する各種光学素子配置の非対称性や光学素子がもつ各種収差等がプローブ誤差となる。通常、プローブ誤差と上記直角度誤差は実際の測定データの中に混在しているので、直角度誤差を正確に決定するには、何らかのデータ処理でプローブ誤差を分離する必要がある。
【００１３】
そこで、プローブ誤差と直角度誤差とを分離して校正する従来例として、特許第２，８９２，８２６号明細書（以下従来例１と称す）に記載される方法を例にとって説明する。この従来例の方法は、▲１▼曲率半径の絶対値が等しく十分な真球度が保証された凹凸の基準球面を用意し、▲２▼特公平７−６９１５８号公報に開示される方法で測定機座標原点を決定し、▲３▼決定された測定機座標においてそれぞれの測定データの理想球面からの形状偏差Ｚｄ（凸）及びＺｄ（凹）を計算し、▲４▼座標軸の直角度誤差による測定誤差Ｅｓを、
【００１４】
Ｅｓ＝（Ｚｄ（凸）＋Ｚｄ（凹））／２　　　　（３）
【００１５】
を用いて計算し、▲５▼この（３）式によって算出したＥｓを、直角度誤差α、βをパラメータとする式　α＾２・Ｒ／２＋α・Ｙ、及び、β＾２・Ｒ／２＋β・Ｘ、で近似することによってα、βを決定し、▲６▼プローブ誤差による測定誤差Ｅｐについては、下記の（４）式を用いて決定する、というものである。
【００１６】
Ｅｐ＝（Ｚｄ（凸）−Ｚｄ（凹））／２　　　　（４）
【００１７】
ここで、直角度誤差αはＸ軸回りの回転、すなわちＹ軸とＺ軸の直角度誤差を表し、βはＹ軸回りの回転、すなわちＸ軸とＺ軸の直角度誤差を表す。
【００１８】
また、特開平１１−８３４５０号（以下従来例２と称す）に記載される方法について説明する。この従来例２の方法は、曲率半径の符号が同一で絶対値が異なる二つの基準球面Ｒ１、Ｒ２を用意し、▲２▼二つの基準球面Ｒ１、Ｒ２の実測データの理想球面に対する形状偏差Ｚｄ（Ｒ１）およびＺｄ（Ｒ２）を求め、▲３▼座標軸の直角度誤差による測定誤差Ｅｓとプローブ誤差による測定誤差Ｅｐを、
【００１９】
Ｅｓ＝（Ｒ１・Ｚｄ（Ｒ１）−Ｒ２・Ｚｄ（Ｒ２））／（Ｒ１−２）　　　　（７）
Ｅｐ＝（Ｒ１・Ｚｄ（Ｒ２）−Ｒ２・Ｚｄ（Ｒ１）／（Ｒ１−Ｒ２）　　　　（８）
を用いて計算する、というものである。
【００２０】
また、特開２０００−７４６６２号（以下従来例３と称す）に記載される方法について説明する。この従来例３の方法は、▲１▼真球度が保証された一つの基準球面を測定し、▲２▼（２’）式のＸ、Ｙ、Ｚにそれぞれ（Ｘ−Ｘｓ）、（Ｙ−Ｙｓ）、（Ｚ−Ｚｓ）を代入した式をモデル式として、実測データとの差を最小化する最適化問題としてα、β、γ、Ｘｓ、Ｙｓ、Ｚｓを求める。
【００２１】
【発明が解決しようとする課題】
しかし、上記従来例１によれば、直角度誤差のうちαとβについては決定できるが、Ｚ軸回りの回転、すなわちＸ軸とＹ軸の直角度誤差γを決定できない点にある。すなわち３個ある直角度誤差のうち２個しか決定できない。この理由を以下に説明する。
【００２２】
基準凸面測定における直角度誤差Ｅｓを、α、β、γによる誤差であるＥ_α（凸）、Ｅ_β（凸）、Ｅ_γ（凸）とに分けて表現し、またプローブ誤差をＥｐ（凸）と表す。同様に、基準凹面測定における直角度誤差α、β、γによる誤差をＥ_α（凹）、Ｅ_β（凹）、Ｅ_γ（凹）、プローブ誤差をＥｐ（凹）と表す。このとき理想球面からの形状偏差Ｚｄ（凸）及びＺｄ（凹）は、下記の（５）式、（６）式でそれぞれ表される。
【００２３】
Ｚｄ（凸）＝Ｅ_α（凸）＋Ｅ_β（凸）＋Ｅ_γ（凸）＋Ｅｐ（凸）　　　（５）
Ｚｄ（凹）＝Ｅ_α（凹）＋Ｅ_β（凹）＋Ｅ_γ（凹）＋Ｅｐ（凹）　　　（６）
【００２４】
そして、基準凹凸面の曲率半径の絶対値が等しいこと、及び、プローブ誤差が被測定面の法線方向に依存した系統誤差であることを考慮すると、Ｅｐ（凹）＝Ｅｐ（凸）^π＝Ｅｐ^πとなる。ここでＥｐ^πは、Ｅｐ（凸）をＺ軸回りにπＲａｄ、すなわち１８０度回転するデータ操作を表す。また、従来例１に記載されているように、Ｅ_α（凹）＝Ｅ_α（凸）＝Ｅ_α、Ｅ_β（凹）＝Ｅ_β（凸）＝Ｅ_βが成り立つ。更に、後述する図６を使って説明するように、Ｅ_γ（凹）＝−Ｅ_γ（凸）＝−Ｅγが成り立つ。これらの関係を上記（５）式、（６）式に代入すると次の（５’）式、（６’）式がそれぞれ得られる。
【００２５】
Ｚｄ（凸）＝Ｅ_α＋Ｅ_β＋Ｅ_γ＋Ｅｐ　　　　（５’）
Ｚｄ（凹）＝Ｅ_α＋Ｅ_β−Ｅ_γ＋Ｅｐ^π　　　（６’）
【００２６】
これらの（５’）式、（６’）式を上記（３）式に代入すると、下記の（３’）式が得られる。
【００２７】
Ｅｓ＝Ｅ_α＋Ｅ_β＋（Ｅｐ＋Ｅｐ^π）／２　　　（３’）
【００２８】
この（３’）式から、γ成分であるＥ_γは相殺されて消えてしまうので原理的にγを決定できないことがわかる。また、α、βについてもＥｐ＝−Ｅｐ^πが成り立つ特殊なケースにおいてしか正しく求められないことがわかる。よって、上記従来例１によれば、３個の直角度誤差のうち２個しか決定できない。すなわち、Ｚ軸回りの回転、すなわちＸ軸とＹ軸の直角度誤差γについては原理的に決定できない。
【００２９】
また、上記従来例２には、（７）式のＥｓから直角度誤差をどのようにして求めるかについての記述がない。更に、プローブ誤差の影響で、直角度誤差の推定値に誤差が混入する。
【００３０】
更に、上記従来例３によれば、プローブ誤差を分離できないことであり、プローブ誤差の大きさ如何では、直角度誤差の推定値α、β、γに無視できないほどの誤差を生じてしまうという問題がある。
【００３１】
本発明はこれらの問題点を解決するためのものであり、プローブ誤差が分離された３個の直角度誤差を決定でき、また直角度誤差を求める演算処理をより単純化できる三次元測定機、三次元測定機の校正方法及び該方法を実行するためのプログラムを格納したコンピュータ読み取り可能な記憶媒体を提供する事を目的とする。
【００３２】
【課題を解決するための手段】
前記問題点を解決するために、被測定面のＺ方向の位置を検知するためのプローブを有する、本発明の三次元測定機の校正方法によれば、真の表面形状が既知で、かつ互いに相似形状を有するＮ個（Ｎは正の整数）の基準測定物の形状を測定し、測定されたＮ個の基準測定物の形状データに基づいて三次元直交座標軸の３個の直角度誤差を検出することに特徴がある。よって、プローブ誤差の影響を排除でき、プローブ誤差がある場合でも３個の直角度誤差α，β，γを精度良く求めることができる。
【００３３】
また、Ｎ個の基準測定物の各形状データに対して、楕円の方程式に近似して３×Ｎ個の直角度誤差を求め、３×Ｎ個の直角度誤差から３個の直角度誤差を検出することにより、プローブ誤差が分離された３個の直角度誤差を求めることができる。
【００３４】
更に、基準測定物の形状データを真の基準測定物の形状に近づける座標変換行列を求め、Ｎ個の座標変換行列の行列要素から３×Ｎ個の直角度誤差を求め、３×Ｎ個の直角度誤差から３個の直角度誤差を検出することにより、直角度誤差を求める演算処理をより単純化できる。
【００３５】
また、基準測定物の形状データと真の表面形状との形状偏差を計算し、Ｎ個の形状偏差データから３個の直角度誤差を検出することにより、直角度誤差を求める演算処理をより単純化できる。
【００３６】
更に、基準測定物の形状データをＺ軸回りに１８０度回転させる座標変換を行うことや、形状偏差データをＺ軸回りに１８０度回転させる座標変換を行うことにより、直角度誤差とプローブ誤差の分離が可能となる。
【００３７】
また、２個の基準測定物を用いることや、基準測定物として曲率半径が異なる基準球を用いることが好ましい。
【００３８】
更に、曲率半径の絶対値が等しく、符号が異なる２個の基準球を用いることにより、曲率半径の絶対値が異なる場合と比較して演算処理を大幅に単純化できる。
【００３９】
また、三次元測定機の座標測定手段の座標測定方向をＸ、Ｙ、Ｚとするとき、基準測定物の中心を通り、かつＸ方向及びＹ方向と非平行をなす、少なくとも２ラインの測定データを用いることにより、必要最小限のデータを使って直角度誤差あるいはプローブ誤差を決定するので、校正作業の手間や時間を節約できる。
【００４０】
更に、別の発明としての、被測定面のＺ方向の位置を検知するためのプローブを有する三次元測定機は、真の表面形状が既知で、かつ互いに相似形状を有するＮ個（Ｎは正の整数）の基準測定物の形状データを記憶する基準測定物形状データ記憶部と、Ｎ個の基準測定物の形状データに基づいて、三次元直交座標軸の３個の直角度誤差を検出するための演算部とを有することに特徴がある。よって、よって、プローブ誤差の影響を排除でき、プローブ誤差がある場合でも３個の直角度誤差α，β，γを精度良く求めることができる。
【００４１】
また、演算部は、基準測定物の形状データと、楕円の方程式との形状偏差を求める演算手段と、収束判定手段と、直角度誤差の数値を改良する改良手段と、Ｎ個の基準測定物の形状データを使って求めた３×Ｎ個の直角度誤差から３個の直角度誤差を演算する直角度誤差演算手段とを有する。よって、プローブ誤差の影響を排除でき、プローブ誤差がある場合でも３個の直角度誤差α，β，γを精度良く求めることができる。
【００４２】
更に、演算部は、直角度誤差を補正する座標変換を基準測定物の形状データに対して行う演算手段と、座標変換後の基準測定物の形状データと真の表面形状の形状偏差を求める演算手段と、収束判定手段と、直角度誤差の数値を改良する改良手段と、Ｎ個の前記基準測定物の形状データを使って求めた３×Ｎ個の直角度誤差から３個の直角度誤差を演算する直角度誤差演算手段とを有する。よって、プローブ誤差の影響を排除でき、プローブ誤差がある場合でも３個の直角度誤差α，β，γを精度良く求めることができる。
【００４３】
また、演算部は、Ｎ個の基準測定物の形状データと、それぞれの真の表面形状との形状偏差を求める演算手段と、Ｎ個の形状偏差データから直角度誤差を演算する直角度誤差演算手段とを有する。よって、プローブ誤差の影響を排除でき、プローブ誤差がある場合でも３個の直角度誤差α，β，γを精度良く求めることができる。
【００４４】
更に、基準測定物の形状データをＺ軸回りに１８０度回転させる座標変換を行う演算手段を有することや、形状偏差データをＺ軸回りに１８０度回転させる座標変換を行う演算手段を有することにより、直角度誤差とプローブ誤差の分離が可能となる。
【００４５】
また、２個の基準測定物を備えたことや、基準測定物として曲率半径が異なる基準球面を備えたことは、三次元測定機において好ましい。
【００４６】
更に、基準測定物として曲率半径の絶対値が等しく、符号が異なる２個の基準球面を備えたことにより、曲率半径の絶対値が異なる場合と比較して演算処理を大幅に単純化できる。
【００４７】
また、別の発明として、コンピュータにより、被測定面のＺ方向の位置を検知するためのプローブを有する三次元測定機の校正方法を実行するためのプログラムを格納したコンピュータ読み取り可能な記憶媒体には、真の表面形状が既知で、かつ互いに相似形状を有するＮ個（Ｎは正の整数）の基準測定物の形状を測定する機能と、測定されたＮ個の基準測定物の形状データに基づいて三次元直交座標軸の３個の直角度誤差を検出する機能とを有する三次元測定機の校正方法を実行するためのプログラムを格納されていることに特徴がある。よって、既存のシステムを変えることなく、三次元測定機の校正システムを汎用的に構築することができる。
【００４８】
また、別の発明としての三次元測定機の校正方法を実行するためのプログラムを格納したコンピュータ読み取り可能な記憶媒体には、直角度誤差をパラメータとするモデル式から擬似データを生成する第１の機能と、基準測定物の形状データと擬似データとの形状偏差を算出する第２の機能と、収束判定する第３の機能と、直角度誤差の数値を改良する第４の機能と、収束判定が完了するまで、第１の機能から第４の機能を繰り返す第５の機能と、Ｎ個の基準測定物の形状データに対して求まる３×Ｎ個の直角度誤差から３個の直角度誤差を算出する第６の機能とを有する三次元測定機の校正方法を実行するためのプログラムが格納されている。よって、既存のシステムを変えることなく、三次元測定機の校正システムを汎用的に構築することができる。
【００４９】
更に、別の発明としての三次元測定機の校正方法を実行するためのプログラムを格納したコンピュータ読み取り可能な記憶媒体には、基準測定物の形状データに対して、直角度誤差を補正する座標変換を行う第１の機能と、座標変換後の基準測定物の形状データと真の基準測定物の形状との形状偏差を算出する第２の機能と、収束判定する第３の機能と、直角度誤差の数値を改良する第４の機能と、収束判定が完了するまで、第１の機能から第４の機能を繰り返す第５の機能と、Ｎ個の基準測定物の形状データに対して求まる３×Ｎ個の直角度誤差から３個の直角度誤差を求める第６の機能とを有する三次元測定機の校正方法を実行するためのプログラムが格納されている。よって、既存のシステムを変えることなく、三次元測定機の校正システムを汎用的に構築することができる。
【００５０】
また、別の発明としての三次元測定機の校正方法を実行するためのプログラムを格納したコンピュータ読み取り可能な記憶媒体には、基準測定物の形状データと真の基準測定物形状との形状偏差を演算させる第１の機能と、Ｎ個の形状偏差データから直角度誤差を演算させる第２の機能とを有する三次元測定機の校正方法を実行するためのプログラムが格納されている。よって、既存のシステムを変えることなく、三次元測定機の校正システムを汎用的に構築することができる。
【００５１】
更に、基準測定物の形状データをＺ軸回りに１８０度回転させる座標変換を行う機能や、形状偏差データをＺ軸回りに１８０度回転させる座標変換を行う機能を有することにより、直角度誤差とプローブ誤差の分離が可能となる三次元測定機の校正システムを汎用的に構築することができる。
【００５２】
また、２個の基準測定物の形状データを処理することにより、直角度誤差とプローブ誤差の分離が可能となる三次元測定機の校正システムを汎用的に構築することができる。
【００５３】
更に、曲率半径が異なる基準球データを処理することが好ましい。
【００５４】
また、曲率半径の絶対値が等しく、符号が異なる２個の基準球データを処理することにより、曲率半径の絶対値が異なる場合と比較して演算処理を大幅に単純化できる三次元測定機の校正システムを汎用的に構築することができる。
【００５５】
【発明の実施の形態】
本発明の三次元測定機の校正方法は、真の表面形状が既知で、かつ互いに相似形状を有するＮ個（Ｎは正の整数）の基準測定物の形状を測定し、測定されたＮ個の基準測定物の形状データに基づいて三次元直交座標軸の３個の直角度誤差を検出する。
【００５６】
【実施例】
はじめに、本発明の実施例について説明する前に、理想球面に対する楕円面の形状偏差の特性について説明する。
図１は一定の直角度誤差における曲率半径別の形状偏差の特性を示す図である。同図において、左の列は直角度誤差α＝１０［μＲａｄ］、中央の列はβ＝１０［μＲａｄ］、右の列はγ＝１０［μＲａｄ］、そして、上段から順に、Ｒ＝−２０ｍｍ（凸面）、Ｒ＝−１０ｍｍ（凸面）、Ｒ＝＋１０ｍｍ（凹面）、Ｒ＝＋２０ｍｍ（凹面）とし、いずれも中心角で±４５度の範囲を図示してある。また、形状偏差の大きさの指標としてＲＭＳ値を各特性毎に示してある。図１からわかることは、第一に、直角度誤差に起因する形状偏差は、測定する対象物の曲率半径に比例して増大する、ということである。第二に、直角度誤差α、β、γに起因する形状偏差をＥ_α、Ｅ_β、Ｅ_γと表し、凸球面の形状偏差Ｅ_α（凸）、Ｅ_β（凸）、Ｅ_γ（凸）と、凹球面の形状偏差Ｅ_α（凹）、Ｅ_β（凹）、Ｅ_γ（凹）を比べると、下記の（９）式、（１０）式、（１１）式が成り立つことがわかる。
【００５７】
Ｅ_α（凸）＝Ｅ_α（凹）＝Ｅ_α　　　　　（９）
Ｅ_β（凸）＝Ｅ_β（凹）＝Ｅ_β　　　　　（１０）
Ｅ_γ（凸）＝−Ｅ_γ（凹）　　　　　　（１１）
【００５８】
第三に、Ｚ軸回りの回転操作に対しては、下記の（１２）式、（１３）式、（１４）式が成り立つことがわかる。
【００５９】
Ｅ_α ^π＝−Ｅ_α　　　　　　　　　（１２）
Ｅ_β ^π＝−Ｅ_β　　　　　　　　　（１３）
Ｅ_γ ^π＝　Ｅ_γ　　　　　　　　　（１４）
【００６０】
但し、Ｅ_α ^π、Ｅ_β ^π、Ｅ_γ ^πは、Ｚ軸回りにπＲａｄ、すなわち１８０度回転するデータ操作を表す。
【００６１】
図２は直角度誤差別の形状偏差の変化を示す特性図である。同図の特性図では、曲率半径を−２０ｍｍ（凸面）に固定し、直角度誤差を変えたときの形状偏差の変化を、ＲＭＳ値の変化として示した。また、対象範囲は中心角で±４５度範囲とした。この図２から、形状偏差は直角度誤差に比例すること、そして直角度誤差γに起因する形状偏差は直角度誤差α、βに起因する形状偏差の約４倍大きいことがわかる。
【００６２】
以上のことから、曲率半径Ｒの理想球面に対する、直角度誤差に起因した形状偏差Ｅｓは下記の（１５）式で表すことができる。
【００６３】
Ｅｓ＝Ｒ（α・Ｅ_α＋β・Ｅ_β＋γ・Ｅ_γ）　　（１５）
【００６４】
Ｒの単位をｍｍ、直角度誤差α、β、γの単位をμＲａｄとすると、（１５）式におけるＥ_α、Ｅ_β、Ｅ_γは、Ｒ＝１ｍｍの理想球面を１μＲａｄの直角度誤差をもつ座標系で測定したときの形状偏差を表している。
【００６５】
以上のことに基づいて本発明の実施例について以下に説明する。
はじめに、曲率半径が異なる２個の基準球を用いる第１の実施例について説明し、既知形状で互いに相似形状を有する３個以上の基準測定物を用いる第２の実施例に説明する。
【００６６】
先ず、曲率半径が異なる２個の基準球として、曲率半径の絶対値がＲ１、Ｒ２の理想凸球面を考える。直角度誤差α、β、γは形状偏差Ｅｓ（Ｒ１）、Ｅｓ（Ｒ２）を生じさせ、そこにさらにプローブ誤差Ｅｐが重畳する。プローブ誤差を含む形状偏差をＺｄ（Ｒ１）、Ｚｄ（Ｒ２）で表すと、プローブ誤差Ｅｐは被測定面の曲率半径によらず一定であることを考慮して、下記の（１６）式、（１７）式を得る。
【００６７】

【００６８】
この（１６）式におけるα１、β１、γ１や、（１７）式におけるα２、β２、γ２は、上述した従来例３と同様の推定演算で決定できる。すなわち、上記（２’）式のＸ、Ｙ、Ｚにそれぞれ（Ｘ−Ｘｓ）、（Ｙ−Ｙｓ）、（Ｚ−Ｚｓ）を代入した式をモデル式とし、実測データとの差を最小化する最適化問題を解くことで、α１、β１、γ１や、α２、β２、γ２を決定する。α１＝α＋Δα／Ｒ１、α２＝α＋Δα／Ｒ２であるから、この２個の式からΔαを消去して、下記の（１８）式を得る。この（１８）式よりプローブ誤差の影響を含まない直角度誤差αが得られる。同様に、下記の（１９）式、（２０）式より、プローブ誤差の影響を含まない直角度誤差β、γが得られる。
【００６９】
α＝（Ｒ１α１−Ｒ２α２）／（Ｒ１−Ｒ２）　　　（１８）
β＝（Ｒ１β１−Ｒ２β２）／（Ｒ１−Ｒ２）　　　（１９）
γ＝（Ｒ１γ１−Ｒ２γ２）／（Ｒ１−Ｒ２）　　　（２０）
【００７０】
次に、曲率半径が異なる２個の基準球として、Ｒ１が凸面、Ｒ２が凹面の場合を考える。ただし、曲率半径の符号は考慮せず絶対値で取り扱うことにする。凹面測定の場合のプローブ誤差は、凸面測定の場合に対して、Ｚ軸回りに１８０度回転するから、α２＝α−Δα／Ｒ２となり、よって下記の（１８’）式が得られる。同様に、β２＝β−Δβ／Ｒ２、γ２＝γ−Δγ／Ｒ２より、下記の（１９’）式、（２０’）式が得られる。
【００７１】
α＝（Ｒ１α１＋Ｒ２α２）／（Ｒ１＋Ｒ２）　　　（１８’）
β＝（Ｒ１β１＋Ｒ２β２）／（Ｒ１＋Ｒ２）　　　（１９’）
γ＝（Ｒ１γ１＋Ｒ２γ２）／（Ｒ１＋Ｒ２）　　　（２０’）
【００７２】
（１８）式、（１９）式、（２０）式と、（１８’）式、（１９’）式、（２０’）式を見比べればわかるように、曲率半径の符号を考慮すれは、基準球面の凹凸に関わらず、（１８）式、（１９）式、（２０）式が成り立つことがわかる。
【００７３】
また、（１８）式、（１９）式、（２０）式から、直角度誤差α、β、γを決定した後、それを（１６）式又は（１７）式に代入することによって、プローブ誤差Ｅｐを正確に求めることも可能である。例えば、（１６）式を使うとすれば、プローブ誤差Ｅｐは下記の（２１）式より得られる。
【００７４】

【００７５】
求めたプローブ誤差は、補正データとして記憶装置に記憶しておき、任意の測定対象の測定データに対するプローブ誤差の補正に利用できる。
【００７６】
次に、曲率半径の異なる３個の基準球面を用いる第２の実施例について説明する。３個の基準球面を使えば、求めたい直角度誤差の真値αに対して、プローブ誤差の影響を含む３個の直角度誤差α１、α２、α３が得られる。
【００７７】
α１＝α＋Δα／Ｒ１　　　　　　　　（２２）
α２＝α＋Δα／Ｒ２　　　　　　　　（２３）
α３＝α＋Δα／Ｒ３　　　　　　　　（２４）
【００７８】
これらの（２２）式、（２３）式、（２４）式は、下記の（２５）式のように表現できる。
【００７９】
【数４】

【００８０】
この（２５）式から、α及びΔαは、最小自乗法を使って下記の（２６）式より求めることができる。
【００８１】
【数５】

【００８２】
但し「−１」は逆行列、「Ｔ」は転置行列を表す。β、γについても同様に求めることができる。また、４個以上の基準球面を用いる場合も、同様の方法で３個の直角度誤差α、β、γを求めることができる。
【００８３】
更に、基準球面の代わりに、互いに相似形状を有する複数の基準測定物を使っても直角度誤差を求めることが可能である。互いに相似形状という条件によって、基準測定物の大きさによらずプローブ誤差は一定となり、上記（１６）式、（１７）式が成り立つからである。
【００８４】
α１、β１、γ１、及びα２、β２、γ２の求め方の部分だけである。第２の実施例の場合は、基準球の実測データをモデル式である楕円の方程式に近似することにより直角度誤差を求めたが、以下説明する第３の実施例では、これとは逆の操作をすることで直角度誤差を求める。
【００８５】
（１）式の座標変換行列Ｑは、理想の座標系における球面を、現実の座標系における楕円面に変換する行列であったから、逆行列Ｑ^{− １}は、楕円面を球面に変換する行列となる。したがって、基準球の実測データにＱ^{− １}の変換を施し、変換後のデータが球面になるように、行列要素に含まれるα、β、γを改良すれば、直角度誤差の最尤推定値が得られる。なお、形状既知であれば、基準測定物が球面以外の場合にも同様の方法が適用できることは言うまでも無い。
【００８６】
ここでは、基準測定物の実測データから理想形状を差し引いた「形状偏差データを」を求め、形状偏差データを使って３個の直角度誤差を決定する方法について説明する。
【００８７】
先ず基準測定物として、曲率半径がＲ１、Ｒ２の２個の理想凸球面を考える。各々の測定データのＸ、Ｙ、Ｚ座標を、各々の曲率半径で除算して曲率半径１ｍｍの測定データにｎｏｒｍａｌｉｚｅする。これは、後で各々の座標データどうしを加減算するので、その前準備としてスケールを合わせておく必要があるからである。ｎｏｒｍａｌｉｚｅしたデータの形状偏差（すなわちＲ＝１ｍｍの理想球面からの形状偏差）は、（１６）式、（１７）式より、下記の（１６’）式、（１７’）式で与えられる。
【００８８】

【００８９】
この（１６’）式、（１７’）式の連立方程式を解いてＥｓが求まる。Ｅｓは、Ｒ＝１ｍｍの球面において直角度誤差のみに起因する形状偏差であるから、ＥｓにＲ＝１ｍｍの理想球面データを加算すれば、楕円面データが得られる。そして、上述した実施例で説明した方法を適用することによって直角度誤差α、β、γを決定できる。
【００９０】
次に、基準測定物として、曲率半径Ｒ１の凸面、Ｒ２の凹面を使う場合を考えてみる。ただし、曲率半径の符号は考慮せず絶対値で取り扱うことにする。凹面測定の場合のプローブ誤差は、凸面測定の場合に対して、Ｚ軸回りに１８０度回転すること、および形状ゆがみの特性、そして上記（９）式〜（１４）式を考慮して、下記の（１６”）式及び（１７”）式を得る。
【００９１】

【００９２】
そして、この（１７”）式をＺ軸回りに１８０度回転して、下記の（１７’’’）式を得る。
【００９３】

【００９４】
（１６”）式と（１７’’’）式の連立方程式を解いてＥｓが求まる。Ｅｓは、Ｒ＝１ｍｍの球面において直角度誤差のみに起因する形状偏差であるから、ＥｓにＲ＝１ｍｍの理想球面データを加算すれば、楕円面データが得られる。そして、第１の実施例や第２の実施例で説明した方法を適用することによって直角度誤差α、β、γを決定できる。
【００９５】
なお、凹凸基準球の一方を１８０度回転させるデータ操作は、上記説明では、形状偏差データに対して行ったが、形状偏差データを求める前の基準球形状データそのものを回転させても構わない。
【００９６】
次に、より一般化して、互いに相似形状を有し、球面でない３個の基準測定物、Ｒ１’、Ｒ２’、Ｒ３’を用いる場合について説明する。但し、Ｒ１’、Ｒ２’、Ｒ３’は、各々の基準測定物の大きさに比例するスケールファクタを表す。この場合、（１６’）式や（１７’）式に相当する式は、以下のように表される。
【００９７】

【００９８】
ここで、直角度誤差に起因する誤差ＥｓやＥｐは、基準測定物が球面である場合とは、プロファイルが異なるので「’」を付けたＥｓ’やＥｐ’で区別して表した。上記（２７）式、（２８）式、（２９）式は、下記の（３０）式のように表現できる。
【００９９】
【数６】

【０１００】
（３０）式から、Ｅｓ’及びＥｐ’は、最小自乗法を使って下記の（３１）式より求めることができる。
【０１０１】
【数７】

【０１０２】
この（３１）式から求まるＥｓ’にスケールファクタＲ’＝１の理想形状データを加算したデータに対して、第１の実施例で説明した方法を適用することによって直角度誤差α、β、γを決定できる。
【０１０３】
また、曲率半径の絶対値が等しい凹凸基準球を用いると、これまでに説明した直角度誤差を求める方法がより単純化できる。
【０１０４】
更に、第１の実施例と第２の実施例で説明した直角度誤差の求め方は、（１８）式、（１９）式、（２０）式を使ったが、曲率半径の絶対値が等しい凹凸基準球を用いる場合には、α＝（α１＋α２）／２、β＝（β１＋β２）／２、γ＝（γ１＋γ２）／２、のように単純になる。
【０１０５】
また、第３の実施例に曲率半径の絶対値が等しい凹凸基準球を用いると、Ｅｓ＝（Ｚｄ（Ｒ１）−Ｚｄ（Ｒ２）^π）／２のように単純になる。
【０１０６】
次に、直角度誤差を求めるために必要な必要最小限のデータについて考える。図１の中央の列のグラフからわかるように、原点（この場合凸基準球の頂点、又は凹基準球のボトムの点が原点である）を通り、Ｘ軸に平行経路で取得された測定データは、直角度誤差βに対する感度だけを有する。逆の言い方をすると、原点を通りＸ軸に平行経路で取得された測定データからは直角度誤差αや直角度誤差γを求めることができない。同様に、図１の左の列のグラフからわかるように、原点を通り、Ｙ軸に平行経路で取得された測定データは、直角度誤差αに対する感度だけを有する。したがって、ともに原点を通り、Ｘ軸及びＹ軸に平行経路で取得されたデータからは、直角度誤差αと直角度誤差βしか求めることができず、直角度誤差γを決定できない。
【０１０７】
そこで、直角度誤差α、β、γを決定するには、原点を通らない測定経路か、あるいは原点を通り、Ｘ軸及びＹ軸に非平行経路で測定データを取得する必要がある。原点を通り、Ｘ軸及びＹ軸に対して４５度±４０度の角度範囲で２本の測定経路を設定すれば、直角度誤差α、β、γの決定が可能である。更に、直角度誤差α、βに起因する形状偏差は、直角度誤差γに起因する形状偏差の４分の１しかないことを考慮すると、望ましくは、Ｘ軸及びＹ軸に対して４５度よりは小さい角度、例えば２０度程度の角度をなす２本の直交経路で測定データを取得するのがよい。
【０１０８】
直角度誤差は定期校正を行う必要があり、三次元測定機の機能の一つとして、自動校正機能を備えているのが望ましい。つまり、曲率半径が異なる２個の基準球の測定データを記憶し、そのデータから直角度誤差を自動で計算する機能を三次元測定機の機能の一つとして備える。
【０１０９】
図３は別の発明の第１の実施例に係る三次元測定機における校正回路の構成を示すブロック図であり、図４は本実施例の三次元測定機における校正回路の動作を示すフローチャートである。両図を用いて本実施例の三次元測定機における校正回路の動作について説明する。
【０１１０】
先ず、図３の直角度誤差初期値設定手段３１により直角度誤差の初期値、α０、β０、γ０を設定する（ステップＳ１０１）。初期値の値は、あとの演算時間をより短く、また局所最適解に陥りにくくするために、できるだけ真のα、β、γに近い値を設定する。例えば、前回校正したときの直角度誤差α、β、γの値を初期値にするとよい。そして、基準球データが一時記憶された図３の基準球データ記憶手段３２から基準球データを読み込む（ステップＳ１０２）。また、図３の楕円面データ生成手段３３により楕円面データを生成する（ステップＳ１０３）。具体的には、上記（２’）式のＸ、Ｙ、Ｚにそれぞれ（Ｘ−Ｘｓ）、（Ｙ−Ｙｓ）、（Ｚ−Ｚｓ）を代入した式から楕円面データを生成する。次に、図３の差分算出手段３４により基準球の実測データと楕円面データの差をとり、差の２乗和を演算する（ステップＳ１０４）。図３の収束判定手段３５により最適解とみなしてよいかどうか判定するために、例えば前回計算した２乗和の値と、最後に計算した２乗和の値の差が十分小さいかどうかみて収束判定を行う（ステップＳ１０５）。収束判定が棄却されれば、図３のパラメータ改良手段３６によりα、β、γ、Ｘｓ、Ｙｓ、Ｚｓ等のパラメータ改良を行い、ステップＳ１０３に戻る（ステップＳ１０５；ＮＯ、ステップＳ１０６）。また、収束判定された場合には、２個の基準球データに対して一連の演算処理を終えたかどうか判定する（ステップＳ１０５；ＹＥＳ、ステップＳ１０７）。一連の演算処理が終わっていないならば、ステップＳ１０２に戻る（ステップＳ１０７；ＮＯ）。一連の演算処理が終了されていれば、第一の基準球データから求めた第一の直角度誤差と、第二の基準球データから求めた第二の直角度誤差を使い、（１８）式、（１９）式、（２０）式等に対応した演算を行うことによって、図３の直角度誤差算出手段３７により最終的な直角度誤差の値を計算する（ステップＳ１０７；ＹＥＳ、ステップＳ１０８）。次に、図３のプローブ誤差算出手段３８により算出された直角度誤差の数値を（１６）式又は（１７式）に代入して、プローブ誤差Ｅｐを求め、求めた直角度誤差及びプローブ誤差の情報を図３の記憶手段３９に記憶させる（ステップＳ１０９，Ｓ１１０）。
【０１１１】
図５は別の発明の第２の実施例に係る三次元測定機における校正回路の構成を示すブロック図であり、図６は本実施例の三次元測定機における校正回路の動作を示すフローチャートである。両図を用いて本実施例の三次元測定機における校正回路の動作について説明する。
【０１１２】
先ず、図５の直角度誤差初期値設定手段５１により直角度誤差の初期値、α０、β０、γ０を設定する（ステップＳ２０１）。初期値の値は、あとの演算時間をより短く、また局所最適解に陥りにくくするために、できるだけ真の直角度誤差α、β、γに近い値を設定する。例えば、前回校正したときの直角度誤差α、β、γの値を初期値にするとよい。そして、基準球データが一時記憶された図５の基準球データ記憶手段５２から基準球データを読み込む（ステップＳ２０２）。次に、読み込んだ基準球データに対して、図５の座標変換手段５３により（１）式の座標変換行列Ｑの逆行列Ｑ^{− １}による座標変換を施す（ステップＳ２０３）。そして、図５の差分算出手段５４により座標変換後の基準球データと理想球面データとの差をとり、差の２乗和を演算する（ステップＳ２０４）。図５の収束判定手段５５により最適解とみなしてよいかどうか判定するために、例えば前回計算した２乗和の値と、最後に計算した２乗和の値の差が十分小さいかどうかみて収束判定を行う（ステップＳ２０５）。収束判定が棄却されれば、図５のパラメータ改良手段５６によりα、β、γ、Ｘｓ、Ｙｓ、Ｚｓ等のパラメータ改良を行い、ステップＳ２０３に戻る（ステップＳ２０５；ＮＯ、ステップＳ２０６）。また、収束判定された場合には、２個の基準球データに対して一連の演算処理を終えたかどうか判定する（ステップＳ２０５；ＹＥＳ、ステップＳ２０７）。一連の演算処理が終わっていないならば、ステップＳ２０２に戻る（ステップＳ２０７；ＮＯ）。一連の演算処理が終了されていれば、第一の基準球データから求めた第一の直角度誤差と、第二の基準球データから求めた第二の直角度誤差を使い、（１８）式、（１９）式、（２０）式等に対応した演算を行うことによって、図５の直角度誤差算出手段５７により最終的な直角度誤差の値を計算する（ステップＳ２０７；ＹＥＳ、ステップＳ２０８）。次に、図５のプローブ誤差算出手段５８により算出された直角度誤差の数値を（１６）式又は（１７式）に代入して、プローブ誤差Ｅｐを求め、求めた直角度誤差及びプローブ誤差の情報を図５の記憶手段５９に記憶させる（ステップＳ２０９，Ｓ２１０）。
【０１１３】
図７は別の発明の第３の実施例に係る三次元測定機における校正回路の構成を示すブロック図であり、図８は本実施例の三次元測定機における校正回路の動作を示すフローチャートである。両図を用いて本実施例の三次元測定機における校正回路の動作について説明する。
【０１１４】
先ず、図７の直角度誤差初期値設定手段７１により理想球面の並進移動量の初期値、Ｘｓ０、Ｙｓ０、Ｚｓ０を設定する（ステップＳ３０１）。次に、基準球データが記憶された図７の基準球データ記憶手段７２から基準球データを読み込む（ステップＳ３０２）。基準球データが凹面か凸面かを判定し、凹面であればＺ軸回りに図７の座標変換手段７３により１８０度回転させる座標変換を行う（ステップＳ３０３）。凹面は回転させずに凸面を回転させるようにしても構わない。そして、図７の球面データ生成手段７４によりＸ、Ｙ、Ｚ方向に、それぞれＸｓ、Ｙｓ、Ｚｓだけ並進移動させた理想球面データを生成する（ステップＳ３０４）。図７の差分算出手段７５により基準球の実測データと理想球面データとの差をとり、差の２乗和を演算する（ステップＳ３０５）。図７の収束判定手段７６により最適解とみなしてよいかどうか判定するための収束判定を行う（ステップＳ３０６）。収束判定が棄却されれば、図７のパラメータ改良手段７７によりＸｓ、Ｙｓ、Ｚｓのパラメータ改良を行い、ステップＳ３０４に戻る（ステップＳ３０６；ＮＯ、ステップＳ３０７）。また、収束判定された場合には、２個の基準球データに対して一連の演算処理を終えたかどうか判定する（ステップＳ３０８）。一連の演算処理を終えていないならば、ステップＳ３０２に戻る（ステップＳ３０８；ＮＯ）。一連の演算処理が終了されていれば、第一の基準球データから求めた第一の形状偏差データと、第二の基準球データから求めた第二の形状偏差データを使い、（２２）式や（２３）式に対応した演算を行うことによって、図７のプローブ誤差算出手段７９によりプローブ誤差を求める（ステップＳ３０８；ＹＥＳ、ステップＳ３０９）。さらに、図７の直角度誤差算出手段７８によりこれを利用して直角度誤差の値を計算する（ステップＳ３１０）。最後に、求めた直角度誤差及びプローブ誤差の情報を図７の記憶手段８０に記憶させる（ステップＳ３１１）。
【０１１５】
図９は別の発明の三次元測定機の構成を示すブロック図である。図１０は本発明の三次元測定機の概略構成を示す図である。図９に示すように、三次元測定機は、３軸直交ステージ９１、形状測定用プローブ９２、座標測定手段９３、制御・演算部９４及び出力部９５を有する。３軸直交ステージ９１は、図１０の（ｃ）に示すような、Ｘ軸ステージ１１１とＹ軸ステージ１１２及びＺ軸ステージ１１３を有し、その上に接触式又は非接触式の形状測定用プローブ９２が取り付けられている。形状測定用プローブ９２と対向する位置には被測定物が固定される。図１０に示すように、測定機の校正時に用いる曲率半径の異なる基準球面１１４、１１５を固定した校正用治具１１６が、位置決めピン１１７，１１８を介して三次元測定機に固定されている。形状測定用プローブ９２は基準球面１１４，１１５の表面を図９の３軸直交ステージ９１の駆動によりならい走査、もしくはｐｏｉｎｔ　ｔｏ　ｐｏｉｎｔで動作する。また、図９における座標測定手段９３は、図１０には図示していないが、例えばレーザ干渉測長器からなり、図１０において、Ｘ軸ステージとＹ軸ステージの移動方向に対して３０度の角度をなすように設置された基準ミラー１１９，１２０を基準としてプローブ先端との距離（図１０中、破線矢印）が逐次測定される。更に、図９の制御・演算部９４は切換部９６、システム制御部９７、校正データ演算部９８及び測定データ補正部９９を有する。切換部９６は座標測定手段９３から入力される座標データの出力先を処理モードに応じて校正データ演算部９８か、または測定データ補正部９９に切り換える。校正データ演算部９８は、上述したように、曲率半径の異なる２個の基準球の測定データを基に、座標軸の直角度誤差（図１０の場合には、３枚の基準ミラー、すなわち基準ミラー１１９，１２０と、不図示のＺ座標測定用基準ミラー間の直角度に相当する）を演算し、またプローブ誤差を演算して、それらの情報を記憶する。測定データ補正部９９は、校正データ演算部９８で求められ、記憶された直角度誤差やプローブ誤差の情報を利用して、基準球以外の被測定物の測定データに対して補正を行う。出力部９５は測定データ補正部９９で直角度誤差補正及びプローブ誤差補正を行った被測定物の形状データに対して、レーザ測長光学系の３０度傾き成分を補正するための座標変換を行った後、表示装置や記憶装置等に出力する。そして、図９のシステム制御部９７は、２個の基準球の設置位置を記憶する記憶手段を備え、基準球の設置位置情報に基づいて、基準球の形状を自動測定させる。図１０の基準球１１４，１１５を固定した校正用治具１１６は、位置決めピン１１７，１１８で位置決めされるので、基準球の設置位置を予め教示しておけばあとは自動測定が可能となる。
【０１１６】
なお、レーザ干渉測長器用基準ミラーが３０度傾いて配置される理由は、上述したように、全ての直角度誤差を求めるために必要な必要最小限のデータは、最も望ましくは、原点を通り、Ｘ軸及びＹ軸に対して３０度の角度をなす２本の直交経路で測定データを取得するのがよいのであって、レーザ干渉測長器の測定座標系を、三次元測定機の装置座標系に対して３０度傾けて配置しておけば、三次元測定機からみればＸＹ座標に平行にプローブを駆動すればよいことになり、斜め３０度の直線補間動作を行わずに済む。もちろん、レーザ干渉測長器用基準ミラーの法線方向が三次元測定機のＸ軸、Ｙ軸と非平行であればよく、実際には４５度±４０度程度の範囲で非平行であればよいのであって、必ずしも３０度に限定されるものではない。
【０１１７】
次に、図１１は本発明のシステム構成を示すブロック図である。つまり、同図は上記実施例における三次元測定機の校正方法によるソフトウェアを実行するマイクロプロセッサ等から構築されるハードウェアを示すものである。同図において、三次元測定機の校正システムはインターフェース（以下Ｉ／Ｆと略す）８１、ＣＰＵ８２、ＲＯＭ８３、ＲＡＭ８４、表示装置８５、ハードディスク８６、キーボード８７及びＣＤ−ＲＯＭドライブ８８を含んで構成されている。また、汎用の処理装置を用意し、ＣＤ−ＲＯＭ８９などの読取可能な記憶媒体には、本発明の三次元測定機の校正方法を実行するプログラムが記憶されている。更に、Ｉ／Ｆ８１を介して外部装置から制御信号が入力され、キーボード８７によって操作者による指令又は自動的に本発明のプログラムが起動される。そして、ＣＰＵ８２は当該プログラムに従って上述の三次元測定機の校正方法に伴う校正制御処理を施し、その処理結果をＲＡＭ８４やハードディスク８６等の記憶装置に格納し、必要により表示装置８５などに出力する。以上のように、本発明の三次元測定機の校正方法を実行するプログラムが記憶した媒体を用いることにより、既存のシステムを変えることなく、三次元測定機の校正システムを汎用的に構築することができる。
【０１１８】
なお、本発明は上記実施例に限定されるものではなく、特許請求の範囲内の記載であれば多種の変形や置換可能であることは言うまでもない。
【０１１９】
【発明の効果】
以上説明したように、被測定面のＺ方向の位置を検知するためのプローブを有する、本発明の三次元測定機の校正方法によれば、真の表面形状が既知で、かつ互いに相似形状を有するＮ個（Ｎは正の整数）の基準測定物の形状を測定し、測定されたＮ個の基準測定物の形状データに基づいて三次元直交座標軸の３個の直角度誤差を検出することに特徴がある。よって、プローブ誤差の影響を排除でき、プローブ誤差がある場合でも３個の直角度誤差α，β，γを精度良く求めることができる。
【０１２０】
また、Ｎ個の基準測定物の各形状データに対して、楕円の方程式に近似して３×Ｎ個の直角度誤差を求め、３×Ｎ個の直角度誤差から３個の直角度誤差を検出することにより、プローブ誤差が分離された３個の直角度誤差を求めることができる。
【０１２１】
更に、基準測定物の形状データを真の基準測定物の形状に近づける座標変換行列を求め、Ｎ個の座標変換行列の行列要素から３×Ｎ個の直角度誤差を求め、３×Ｎ個の直角度誤差から３個の直角度誤差を検出することにより、直角度誤差を求める演算処理をより単純化できる。
【０１２２】
また、基準測定物の形状データと真の表面形状との形状偏差を計算し、Ｎ個の形状偏差データから３個の直角度誤差を検出することにより、直角度誤差を求める演算処理をより単純化できる。
【０１２３】
更に、基準測定物の形状データをＺ軸回りに１８０度回転させる座標変換を行うことや、形状偏差データをＺ軸回りに１８０度回転させる座標変換を行うことにより、直角度誤差とプローブ誤差の分離が可能となる。
【０１２４】
また、２個の基準測定物を用いることや、基準測定物として曲率半径が異なる基準球を用いることが好ましい。
【０１２５】
更に、曲率半径の絶対値が等しく、符号が異なる２個の基準球を用いることにより、曲率半径の絶対値が異なる場合と比較して演算処理を大幅に単純化できる。
【０１２６】
また、三次元測定機の座標測定手段の座標測定方向をＸ、Ｙ、Ｚとするとき、基準測定物の中心を通り、かつＸ方向及びＹ方向と非平行をなす、少なくとも２ラインの測定データを用いることにより、必要最小限のデータを使って直角度誤差あるいはプローブ誤差を決定するので、校正作業の手間や時間を節約できる。
【０１２７】
更に、別の発明としての、被測定面のＺ方向の位置を検知するためのプローブを有する三次元測定機は、真の表面形状が既知で、かつ互いに相似形状を有するＮ個（Ｎは正の整数）の基準測定物の形状データを記憶する基準測定物形状データ記憶部と、Ｎ個の基準測定物の形状データに基づいて、三次元直交座標軸の３個の直角度誤差を検出するための演算部とを有することに特徴がある。よって、よって、プローブ誤差の影響を排除でき、プローブ誤差がある場合でも３個の直角度誤差α，β，γを精度良く求めることができる。
【０１２８】
また、演算部は、基準測定物の形状データと、楕円の方程式との形状偏差を求める演算手段と、収束判定手段と、直角度誤差の数値を改良する改良手段と、Ｎ個の基準測定物の形状データを使って求めた３×Ｎ個の直角度誤差から３個の直角度誤差を演算する直角度誤差演算手段とを有する。よって、プローブ誤差の影響を排除でき、プローブ誤差がある場合でも３個の直角度誤差α，β，γを精度良く求めることができる。
【０１２９】
更に、演算部は、直角度誤差を補正する座標変換を基準測定物の形状データに対して行う演算手段と、座標変換後の基準測定物の形状データと真の表面形状の形状偏差を求める演算手段と、収束判定手段と、直角度誤差の数値を改良する改良手段と、Ｎ個の前記基準測定物の形状データを使って求めた３×Ｎ個の直角度誤差から３個の直角度誤差を演算する直角度誤差演算手段とを有する。よって、プローブ誤差の影響を排除でき、プローブ誤差がある場合でも３個の直角度誤差α，β，γを精度良く求めることができる。
【０１３０】
また、演算部は、Ｎ個の基準測定物の形状データと、それぞれの真の表面形状との形状偏差を求める演算手段と、Ｎ個の形状偏差データから直角度誤差を演算する直角度誤差演算手段とを有する。よって、プローブ誤差の影響を排除でき、プローブ誤差がある場合でも３個の直角度誤差α，β，γを精度良く求めることができる。
【０１３１】
更に、基準測定物の形状データをＺ軸回りに１８０度回転させる座標変換を行う演算手段を有することや、形状偏差データをＺ軸回りに１８０度回転させる座標変換を行う演算手段を有することにより、直角度誤差とプローブ誤差の分離が可能となる。
【０１３２】
また、２個の基準測定物を備えたことや、基準測定物として曲率半径が異なる基準球面を備えたことは、三次元測定機において好ましい。
【０１３３】
更に、基準測定物として曲率半径の絶対値が等しく、符号が異なる２個の基準球面を備えたことにより、曲率半径の絶対値が異なる場合と比較して演算処理を大幅に単純化できる。
【０１３４】
また、別の発明として、コンピュータにより、被測定面のＺ方向の位置を検知するためのプローブを有する三次元測定機の校正方法を実行するためのプログラムを格納したコンピュータ読み取り可能な記憶媒体には、真の表面形状が既知で、かつ互いに相似形状を有するＮ個（Ｎは正の整数）の基準測定物の形状を測定する機能と、測定されたＮ個の基準測定物の形状データに基づいて三次元直交座標軸の３個の直角度誤差を検出する機能とを有する三次元測定機の校正方法を実行するためのプログラムを格納されていることに特徴がある。よって、既存のシステムを変えることなく、三次元測定機の校正システムを汎用的に構築することができる。
【０１３５】
また、別の発明としての三次元測定機の校正方法を実行するためのプログラムを格納したコンピュータ読み取り可能な記憶媒体には、直角度誤差をパラメータとするモデル式から擬似データを生成する第１の機能と、基準測定物の形状データと擬似データとの形状偏差を算出する第２の機能と、収束判定する第３の機能と、直角度誤差の数値を改良する第４の機能と、収束判定が完了するまで、第１の機能から第４の機能を繰り返す第５の機能と、Ｎ個の基準測定物の形状データに対して求まる３×Ｎ個の直角度誤差から３個の直角度誤差を算出する第６の機能とを有する三次元測定機の校正方法を実行するためのプログラムが格納されている。よって、既存のシステムを変えることなく、三次元測定機の校正システムを汎用的に構築することができる。
【０１３６】
更に、別の発明としての三次元測定機の校正方法を実行するためのプログラムを格納したコンピュータ読み取り可能な記憶媒体には、基準測定物の形状データに対して、直角度誤差を補正する座標変換を行う第１の機能と、座標変換後の基準測定物の形状データと真の基準測定物の形状との形状偏差を算出する第２の機能と、収束判定する第３の機能と、直角度誤差の数値を改良する第４の機能と、収束判定が完了するまで、第１の機能から第４の機能を繰り返す第５の機能と、Ｎ個の基準測定物の形状データに対して求まる３×Ｎ個の直角度誤差から３個の直角度誤差を求める第６の機能とを有する三次元測定機の校正方法を実行するためのプログラムが格納されている。よって、既存のシステムを変えることなく、三次元測定機の校正システムを汎用的に構築することができる。
【０１３７】
また、別の発明としての三次元測定機の校正方法を実行するためのプログラムを格納したコンピュータ読み取り可能な記憶媒体には、基準測定物の形状データと真の基準測定物形状との形状偏差を演算させる第１の機能と、Ｎ個の形状偏差データから直角度誤差を演算させる第２の機能とを有する三次元測定機の校正方法を実行するためのプログラムが格納されている。よって、既存のシステムを変えることなく、三次元測定機の校正システムを汎用的に構築することができる。
【０１３８】
更に、基準測定物の形状データをＺ軸回りに１８０度回転させる座標変換を行う機能や、形状偏差データをＺ軸回りに１８０度回転させる座標変換を行う機能を有することにより、直角度誤差とプローブ誤差の分離が可能となる三次元測定機の校正システムを汎用的に構築することができる。
【０１３９】
また、２個の基準測定物の形状データを処理することにより、直角度誤差とプローブ誤差の分離が可能となる三次元測定機の校正システムを汎用的に構築することができる。
【０１４０】
更に、曲率半径が異なる基準球データを処理することが好ましい。
【０１４１】
また、曲率半径の絶対値が等しく、符号が異なる２個の基準球データを処理することにより、曲率半径の絶対値が異なる場合と比較して演算処理を大幅に単純化できる三次元測定機の校正システムを汎用的に構築することができる。
【図面の簡単な説明】
【図１】一定の直角度誤差における曲率半径別の形状偏差の特性を示す図である。
【図２】直角度誤差別の形状偏差の変化を示す特性図である。
【図３】別の発明の第１の実施例に係る三次元測定機における校正回路の構成を示すブロック図である。
【図４】第１の実施例の三次元測定機における校正回路の動作を示すフローチャートである。
【図５】別の発明の第２の実施例に係る三次元測定機における校正回路の構成を示すブロック図である。
【図６】第２の実施例の三次元測定機における校正回路の動作を示すフローチャートである。
【図７】別の発明の第３の実施例に係る三次元測定機における校正回路の構成を示すブロック図である。
【図８】第３の実施例の三次元測定機における校正回路の動作を示すフローチャートである。
【図９】別の発明の三次元測定機の構成を示すブロック図である。
【図１０】別の発明の三次元測定機の概略構成を示す図である。
【図１１】本発明のシステム構成を示すブロック図である。
【図１２】接触式プローブの構成を示す概略図である。
【図１３】非接触式プローブの構成を示す概略図である。
【図１４】３軸の座標軸直角度誤差を説明する図である。
【符号の説明】
３１，５１，７１；直角度誤差初期値設定手段、３２，５２，７２；基準球データ記憶手段、３３；楕円面データ生成手段、３４，５４，７５；差分算出手段、３５，５５，７６；収束判定手段、３６，５６，７７；パラメータ改良手段、３７，５７，７８；直角度誤差算出手段、３８，５８，７９；プローブ誤差算出手段、３９，５９，８０；記憶手段、５３，７３；座標変換手段、７４；球面データ生成手段、９１；３軸直交ステージ、９２；形状測定用プローブ、９３；座標測定手段、９４；制御・演算部、９５；出力部、９６；切換部、９７；システム制御部、９８；校正データ演算部、９９；測定データ補正部、１００，２００；光プローブ。[0001]
TECHNICAL FIELD OF THE INVENTION
The present invention relates to a coordinate measuring machine, a method of calibrating the coordinate measuring machine, and a computer-readable storage medium storing a program for executing the method, and more particularly to an optical element such as a lens, particularly an aspherical shape. The present invention relates to a method of calibrating a coordinate axis squareness error in three axes when measuring is performed.
[0002]
[Prior art]
A typical method for measuring the shape of an aspherical lens or the like is to provide a probe on a three-axis orthogonal stage having an X-axis stage, a Y-axis stage, and a Z-axis stage, and fix an object to be measured at a position facing the probe. Then, the three-axis orthogonal stage is driven, and the surface of the workpiece is scanned by the probe. As a scanning method, there are a scanning operation method and a point-to-point method in which an approach operation and a retreat operation are repeated for each point. Then, by sequentially measuring the position of the probe during scanning using a laser length measuring device or the like, the shape of the surface of the measured object is acquired as coordinate point sequence data.
[0003]
Here, the probe will be described. The probe can be roughly classified into a contact type and a non-contact type. First, the contact type probe will be described. In FIG. 12 showing the configuration of the contact type probe, the contact type optical probe 100 has a contact 103 elastically supported in a thrust direction by a spring 102 with respect to a housing 101. The air is sucked into the porous material 105 through the suction port 104 to form a static pressure air guide for the contact 103. A true sphere 106 is fixed to the tip of the contact 103 that contacts the surface 108 to be measured, and a displacement gauge 107 is provided at a position facing the opposite end surface. When a three-axis orthogonal stage (not shown) to which the housing 101 is fixed is driven to press the true sphere 106 at the tip of the contact 103 against the surface 108 to be measured, the spring 102 is deformed and the output of the displacement meter 107 is changed. Change. Therefore, the surface to be measured 108 is scanned while controlling the output of the displacement meter 107 by driving the three-axis orthogonal stage, and at the same time, the position of the probe 100 being scanned is sequentially determined using a laser measuring device or the like. By measuring, the shape of the surface 108 to be measured is measured. Further, by adding a slight output variation of the displacement meter 107 during scanning to the output of the laser length measuring device or the like, it is possible to correct a follow-up error of the probe 100 with respect to irregularities on the surface 108 to be measured, thereby achieving higher accuracy. Measurement can be performed.
[0004]
Next, an optical probe is used as a typical example of a non-contact probe. In FIG. 13 showing a configuration of a non-contact type probe, a non-contact type optical probe 200 sends light emitted from a light source 201 to a lens 203 via a half mirror 202, and the lens 203 puts a light of about several μm on a surface 205 to be measured. Focus on a small spot. The light reflected on the surface to be measured 205 passes through the lens 203 and the half mirror 202 again, and is guided to the focus detection system 204. As the focus detection system 204, for example, an optical system similar to a pickup of an optical disk drive is used, and an electric signal corresponding to a distance from the measured surface 205 is output. The three-axis orthogonal stage to which the optical probe 200 is attached is driven to bring the optical probe 200 close to the surface to be measured 205 to capture an output signal, and to measure while controlling the three-axis orthogonal stage so that the output signal is constant. The surface 205 is scanned, and the position of the optical probe 200 during the scanning is sequentially measured using a laser length measuring device or the like to measure the shape of the object to be measured.
[0005]
When measuring the shape by scanning the surface to be measured using such a contact or non-contact probe, the squareness of the X, Y, and Z axes of the measurement coordinate system affects the measurement accuracy and is ignored. It is known that measurement errors can occur to the extent that they cannot be performed. For example, when defining three coordinate axis squareness errors α, β, and γ as shown in FIG. 14, the coordinates of an arbitrary point P in an ideal orthogonal coordinate system (X0, Y0, Z0) that does not include squareness errors. (PX0, pY0, pZ0) is mapped to (pX, pY, pZ) in the actual coordinate system (X, Y, Z) including the squareness error, and (pX0, pY0, pZ0) and (pX, pY, pZ0) ), The following equation (1) holds.
[0006]
(Equation 1)

(1)
[0007]
Here, (is, js, ks) indicates a unit vector in the s direction, and Q is a coordinate transformation matrix from an ideal rectangular coordinate system to a real coordinate system. At this time, a set of points P at a distance R from the origin in the ideal coordinate system, that is, a spherical surface with a radius R is expressed by an inner product of the following equation (2) in the actual coordinate system (X, Y, Z). Surface.
[0008]
(Equation 2)

[0009]
When this equation (2) is expressed by an explicit function, the following equation (2 ') is obtained in consideration of α << 1, β << 1, and γ << 1.
[0010]
(Equation 3)

(2 ')
[0011]
Equation (2 ') indicates that the spherical surface in the ideal coordinate system is mapped to an ellipsoid in the actual coordinate system by the coordinate transformation matrix Q in equation (1). That is, if the squareness of the measurement coordinate system is out of order, the spherical surface is measured as an elliptical surface. Therefore, in the actual operation of the CMM, α, β, and γ are obtained by calibration performed in advance, and the inverse transformation Q is calculated with respect to the coordinates (pX, pY, pZ) measured in the actual coordinate system.^-1Is performed to correct the measurement data.
[0012]
In the shape measurement method using such a probe, a probe error occurs in addition to the squareness error. If this probe error cannot be neglected with respect to the desired measurement accuracy, it is necessary to correct the probe error, so that the probe error needs to be measured. Here, the probe error refers to a system error that is caused by the probe and depends on the normal direction of the surface to be measured. Specifically, in the case of a contact probe, the sphericity error of the probe tip sphere, and in the case of using an optical displacement meter as a contacted probe, the arrangement of various optical elements with respect to the optical axis of the optical displacement meter. Asymmetry, various aberrations of the optical element, and the like become probe errors. Usually, the probe error and the squareness error are mixed in the actual measurement data. Therefore, in order to accurately determine the squareness error, it is necessary to separate the probe error by some data processing.
[0013]
Therefore, as a conventional example of calibrating the probe error and the squareness error separately, a method described in Japanese Patent No. 2,892,826 (hereinafter referred to as Conventional Example 1) will be described as an example. According to the method of this conventional example, (1) a reference spherical surface having irregularities, in which the absolute values of the curvature radii are equal and sufficient sphericity is guaranteed, is prepared, and (2) a method disclosed in Japanese Patent Publication No. 7-69158. (3) Calculate the shape deviations Zd (convex) and Zd (concave) of the respective measurement data from the ideal sphere at the determined measuring machine coordinates, and (4) squareness error of the coordinate axes. The measurement error Es by
[0014]
Es = (Zd (convex) + Zd (concave)) / 2 (3)
[0015]
(5) The Es calculated by the equation (3) is calculated by using the equations {α ＾ 2 · R / 2 + α · Y and β ＾ 2 · R / 2 + β using the squareness errors α and β as parameters. Α and β are determined by approximation with X, and (6) the measurement error Ep due to the probe error is determined using the following equation (4).
[0016]
Ep = (Zd (convex) −Zd (concave)) / 2 (4)
[0017]
Here, the squareness error α represents the rotation around the X axis, that is, the squareness error between the Y axis and the Z axis, and β represents the rotation around the Y axis, that is, the squareness error between the X axis and the Z axis.
[0018]
Further, a method described in JP-A-11-83450 (hereinafter referred to as Conventional Example 2) will be described. In the method of Conventional Example 2, two reference spheres R1 and R2 having the same sign of curvature radius but different absolute values are prepared, and (2) the shape deviation Zd of the measured data of the two reference spheres R1 and R2 with respect to the ideal sphere. (R1) and Zd (R2) are obtained, and (3) the measurement error Es due to the squareness error of the coordinate axis and the measurement error Ep due to the probe error are calculated as follows:
[0019]
Es = (R1 · Zd (R1) −R2 · Zd (R2)) / (R1-2) (7)
Ep = (R1 · Zd (R2) −R2 · Zd (R1) / (R1−R2) (8)
Is calculated using
[0020]
A method described in JP-A-2000-74662 (hereinafter, referred to as Conventional Example 3) will be described. In the method of Conventional Example 3, (1) one reference spherical surface whose sphericity is guaranteed is measured, and (X−Xs) and (Y) are respectively assigned to X, Y, and Z of the expression (2) (2 ′). −Ys) and (Z−Zs) are substituted into a model formula, and α, β, γ, Xs, Ys and Zs are obtained as an optimization problem for minimizing the difference from the measured data.
[0021]
[Problems to be solved by the invention]
However, according to the conventional example 1, although α and β can be determined among the squareness errors, rotation about the Z axis, that is, squareness error γ between the X axis and the Y axis cannot be determined. That is, only two of the three squareness errors can be determined. The reason will be described below.
[0022]
The squareness error Es in the reference convex surface measurement is represented by an error E due to α, β, γ._α(Convex), E_β(Convex), E_γ(Convex) and the probe error is represented as Ep (convex). Similarly, errors due to squareness errors α, β, and γ in the reference concave surface measurement are represented by E_α(Concave), E_β(Concave), E_γ(Concave), and the probe error is represented by Ep (concave). At this time, the shape deviations Zd (convex) and Zd (concave) from the ideal spherical surface are expressed by the following equations (5) and (6), respectively.
[0023]
Zd (convex) = E_α(Convex) + E_β(Convex) + E_γ(Convex) + Ep (convex) (5)
Zd (concave) = E_α(Concave) + E_β(Concave) + E_γ(Concave) + Ep (Concave) (6)
[0024]
Considering that the absolute values of the radii of curvature of the reference uneven surface are equal and that the probe error is a systematic error depending on the normal direction of the measured surface, Ep (concave) = Ep (convex)^π= Ep^πIt becomes. Where Ep^πRepresents a data operation in which Ep (convex) is rotated by πRad around the Z axis, that is, 180 degrees. Further, as described in Conventional Example 1, E_α(Concave) = E_α(Convex) = E_α, E_β(Concave) = E_β(Convex) = E_βHolds. Further, as described with reference to FIG._γ(Concave) =-E_γ(Convex) = − Eγ holds. By substituting these relationships into the above equations (5) and (6), the following equations (5 ') and (6') are obtained, respectively.
[0025]
Zd (convex) = E_α+ E_β+ E_γ+ Ep (5 ’)
Zd (concave) = E_α+ E_β-E_γ+ Ep^π(6 ’)
[0026]
By substituting the equations (5 ') and (6') into the equation (3), the following equation (3 ') is obtained.
[0027]
Es = E_α+ E_β+ (Ep + Ep^π) / 2 '(3')
[0028]
From this equation (3 ′), it is found that the γ component E_γIt can be understood that γ cannot be determined in principle because γ is canceled out and disappears. Also, for α and β, Ep = −Ep^πIt can be seen that it can be correctly obtained only in the special case where Therefore, according to Conventional Example 1, only two of the three squareness errors can be determined. That is, the rotation about the Z axis, that is, the squareness error γ between the X axis and the Y axis cannot be determined in principle.
[0029]
Further, in the above-mentioned conventional example 2, there is no description on how to determine the squareness error from Es in equation (7). Further, due to the effect of the probe error, an error is mixed in the estimated value of the squareness error.
[0030]
Further, according to the above-described conventional example 3, the probe error cannot be separated, and the problem that the estimated values α, β, and γ of the squareness errors may not be neglected depending on the magnitude of the probe error. There is.
[0031]
The present invention has been made to solve these problems, and a three-dimensional measuring machine capable of determining three squareness errors from which a probe error is separated, and further simplifying an arithmetic process for determining the squareness error, An object of the present invention is to provide a method of calibrating a coordinate measuring machine and a computer-readable storage medium storing a program for executing the method.
[0032]
[Means for Solving the Problems]
In order to solve the above problem, according to the calibration method of the coordinate measuring machine of the present invention, which has a probe for detecting the position of the surface to be measured in the Z direction, the true surface shapes are known and mutually The shapes of N (N is a positive integer) reference objects having similar shapes are measured, and three squareness errors of the three-dimensional orthogonal coordinate axes are determined based on the measured shape data of the N reference objects. The feature is to detect. Therefore, the influence of the probe error can be eliminated, and the three squareness errors α, β, γ can be obtained with high accuracy even when there is a probe error.
[0033]
Further, for each shape data of the N reference measurement objects, 3 × N squareness errors are obtained by approximating the equation of an ellipse, and three squareness errors are calculated from the 3 × N squareness errors. By detecting, three squareness errors from which the probe error is separated can be obtained.
[0034]
Further, a coordinate conversion matrix that brings the shape data of the reference object closer to the shape of the true reference object is obtained, and 3 × N squareness errors are obtained from matrix elements of the N coordinate conversion matrices. By detecting three squareness errors from the squareness error, the calculation process for determining the squareness error can be further simplified.
[0035]
In addition, by calculating the shape deviation between the shape data of the reference object and the true surface shape, and detecting three squareness errors from the N shape deviation data, the calculation process for obtaining the squareness error is simplified. Can be
[0036]
Further, by performing coordinate conversion for rotating the shape data of the reference measurement object by 180 degrees around the Z axis and by performing coordinate conversion for rotating the shape deviation data by 180 degrees around the Z axis, the squareness error and the probe error can be reduced. Separation becomes possible.
[0037]
Further, it is preferable to use two reference measurement objects or to use reference spheres having different radii of curvature as the reference measurement objects.
[0038]
Further, by using two reference spheres having the same absolute value of the radius of curvature and different signs, the calculation process can be greatly simplified as compared with the case where the absolute values of the radius of curvature are different.
[0039]
When the coordinate measuring directions of the coordinate measuring means of the coordinate measuring machine are X, Y, and Z, at least two lines of measurement data passing through the center of the reference object and being non-parallel to the X and Y directions. Is used to determine the squareness error or the probe error using the minimum necessary data, so that the labor and time for the calibration work can be saved.
[0040]
Further, as another invention, a three-dimensional measuring machine having a probe for detecting a position of a surface to be measured in the Z direction is a N-dimensional measuring machine having a true surface shape known and having similar shapes to each other (N is a positive number). ) For detecting three squareness errors of the three-dimensional orthogonal coordinate axes based on the shape data of the reference object shape data storage unit for storing the shape data of the reference object of the reference object). And an arithmetic unit. Therefore, the influence of the probe error can be eliminated, and even when there is a probe error, the three squareness errors α, β, and γ can be accurately obtained.
[0041]
The calculating unit includes calculating means for calculating a shape deviation between the shape data of the reference measured object and the equation of the ellipse, convergence determining means, improving means for improving the numerical value of the squareness error, and N reference measured objects. Squareness error calculating means for calculating three squareness errors from 3 × N squareness errors obtained by using the shape data of (3). Therefore, the influence of the probe error can be eliminated, and the three squareness errors α, β, γ can be obtained with high accuracy even when there is a probe error.
[0042]
Further, the calculation unit is configured to perform a coordinate conversion for correcting the squareness error on the shape data of the reference object, and an operation for obtaining a shape deviation between the shape data of the reference object after the coordinate conversion and the true surface shape. Means, convergence determining means, improving means for improving the numerical value of the squareness error, and three squareness errors from 3 × N squareness errors obtained using the shape data of the N reference objects. Is calculated. Therefore, the influence of the probe error can be eliminated, and the three squareness errors α, β, γ can be obtained with high accuracy even when there is a probe error.
[0043]
The calculating unit is configured to calculate shape data of the N pieces of reference workpieces and a shape deviation between each of the true surface shapes, and to calculate a squareness error from the N pieces of shape deviation data. Means. Therefore, the influence of the probe error can be eliminated, and the three squareness errors α, β, γ can be obtained with high accuracy even when there is a probe error.
[0044]
Further, by having an arithmetic means for performing coordinate conversion for rotating the shape data of the reference measurement object by 180 degrees about the Z axis, and by having an arithmetic means for performing coordinate conversion for rotating the shape deviation data by 180 degrees about the Z axis, And the squareness error and the probe error can be separated.
[0045]
Further, it is preferable for the coordinate measuring machine to have two reference measurement objects or to have a reference spherical surface having a different radius of curvature as the reference measurement object.
[0046]
Furthermore, by providing two reference spheres having the same absolute value of the radius of curvature and different signs as the reference measurement object, the arithmetic processing can be greatly simplified as compared with the case where the absolute values of the radius of curvature are different.
[0047]
According to another aspect of the present invention, there is provided a computer-readable storage medium storing a program for executing a method of calibrating a coordinate measuring machine having a probe for detecting a position of a surface to be measured in a Z direction by a computer. A function of measuring the shapes of N (N is a positive integer) reference measurement objects whose true surface shapes are known and similar to each other, and based on the measured shape data of the N reference measurement objects. And a program for executing a method of calibrating a three-dimensional measuring machine having a function of detecting three squareness errors of three-dimensional orthogonal coordinate axes. Therefore, the calibration system of the coordinate measuring machine can be universally constructed without changing the existing system.
[0048]
Further, a computer-readable storage medium storing a program for executing a method of calibrating a coordinate measuring machine as another invention has a first data for generating pseudo data from a model formula having a squareness error as a parameter. A function, a second function for calculating a shape deviation between shape data and pseudo data of the reference measurement object, a third function for determining convergence, a fourth function for improving the numerical value of the squareness error, and a convergence determination And a fifth function of repeating the first to fourth functions until the completion of the calculation, and three squareness errors from 3 × N squareness errors obtained for the shape data of the N reference measurement objects. The program for executing the method of calibrating the coordinate measuring machine having the sixth function of calculating the CMM is stored. Therefore, the calibration system of the coordinate measuring machine can be universally constructed without changing the existing system.
[0049]
Further, a computer-readable storage medium storing a program for executing a method of calibrating a coordinate measuring machine as another invention includes a coordinate transformation for correcting a squareness error with respect to shape data of a reference measurement object. A second function of calculating the shape deviation between the shape data of the reference object after coordinate conversion and the shape of the true reference object, a third function of determining convergence, A fourth function for improving the numerical value of the error, a fifth function for repeating the first to fourth functions until the convergence determination is completed, and a third function for the shape data of the N reference measurement objects. A program for executing a method of calibrating a coordinate measuring machine having a sixth function of obtaining three squareness errors from × N squareness errors is stored. Therefore, the calibration system of the coordinate measuring machine can be universally constructed without changing the existing system.
[0050]
Further, a computer-readable storage medium storing a program for executing the calibration method of the coordinate measuring machine as another invention includes a shape deviation between the shape data of the reference object and the shape of the true reference object. A program for executing a method of calibrating a coordinate measuring machine having a first function for calculating and a second function for calculating a squareness error from N shape deviation data is stored. Therefore, the calibration system of the coordinate measuring machine can be universally constructed without changing the existing system.
[0051]
Further, by having a function of performing coordinate conversion for rotating the shape data of the reference measurement object by 180 degrees about the Z axis and a function of performing coordinate conversion for rotating the shape deviation data by 180 degrees about the Z axis, squareness error and A calibration system for a coordinate measuring machine capable of separating a probe error can be universally constructed.
[0052]
Further, by processing the shape data of the two reference measurement objects, a calibration system of the coordinate measuring machine that can separate the squareness error and the probe error can be constructed for general use.
[0053]
Further, it is preferable to process reference sphere data having different radii of curvature.
[0054]
In addition, by processing two reference sphere data having the same absolute value of the radius of curvature and different signs, the operation of the three-dimensional measuring device can be greatly simplified as compared with the case where the absolute value of the radius of curvature is different. A calibration system can be universally constructed.
[0055]
BEST MODE FOR CARRYING OUT THE INVENTION
The method for calibrating a coordinate measuring machine according to the present invention measures the shapes of N (N is a positive integer) reference measurement objects whose true surface shapes are known and have similar shapes to each other. The three squareness errors of the three-dimensional orthogonal coordinate axis are detected based on the shape data of the reference object.
[0056]
【Example】
First, before describing the embodiments of the present invention, the characteristics of the shape deviation of an elliptical surface with respect to an ideal spherical surface will be described.
FIG. 1 is a diagram showing characteristics of a shape deviation for each radius of curvature at a constant squareness error. In the figure, the squareness error α = 10 [μRad] in the left column, β = 10 [μRad] in the center column, γ = 10 [μRad] in the right column, and R = −20 mm in order from the top. (Convex surface), R = −10 mm (convex surface), R = + 10 mm (concave surface), and R = + 20 mm (concave surface), all of which show a range of ± 45 degrees in central angle. Also, the RMS value is shown for each characteristic as an index of the magnitude of the shape deviation. It can be seen from FIG. 1 that, firstly, the shape deviation due to the squareness error increases in proportion to the radius of curvature of the object to be measured. Second, the shape deviation caused by the squareness errors α, β, γ is expressed by E_α, E_β, E_γAnd the shape deviation E of the convex spherical surface_α(Convex), E_β(Convex), E_γ(Convex) and the shape deviation E of the concave spherical surface_α(Concave), E_β(Concave), E_γComparing (concave), it can be seen that the following equations (9), (10), and (11) hold.
[0057]
E_α(Convex) = E_α(Concave) = E_α(9)
E_β(Convex) = E_β(Concave) = E_β(10)
E_γ(Convex) =-E_γ(Concave) (11)
[0058]
Third, it can be seen that the following expressions (12), (13), and (14) hold for the rotation operation about the Z axis.
[0059]
E_α ^π= -E_α(12)
E_β ^π= -E_β(13)
E_γ ^π= E_γ(14)
[0060]
Where E_α ^π, E_β ^π, E_γ ^πRepresents πRad about the Z axis, that is, a data operation rotated by 180 degrees.
[0061]
FIG. 2 is a characteristic diagram showing a change in shape deviation for each squareness error. In the characteristic diagram of FIG. 3, a change in the shape deviation when the radius of curvature is fixed to −20 mm (convex surface) and the squareness error is changed is shown as a change in the RMS value. The target range was a range of ± 45 degrees at the central angle. It can be seen from FIG. 2 that the shape deviation is proportional to the squareness error, and that the shape deviation caused by the squareness error γ is about four times larger than the shape deviation caused by the squareness errors α and β.
[0062]
From the above, the shape deviation Es due to the squareness error with respect to the ideal spherical surface having the radius of curvature R can be expressed by the following equation (15).
[0063]
Es = R (α · E_α+ Β · E_β+ Γ · E_γ) (15)
[0064]
Assuming that the unit of R is mm and the unit of the squareness errors α, β, γ is μRad, E in equation (15)_α, E_β, E_γRepresents a shape deviation when an ideal spherical surface of R = 1 mm is measured in a coordinate system having a squareness error of 1 μRad.
[0065]
Embodiments of the present invention will be described below based on the above.
First, a first embodiment using two reference spheres having different radii of curvature will be described, and a second embodiment using three or more reference objects having known shapes and similar shapes will be described.
[0066]
First, as two reference spheres having different radii of curvature, an ideal convex sphere having absolute values of the radii of curvature R1 and R2 is considered. The squareness errors α, β, γ cause shape deviations Es (R1), Es (R2), on which the probe error Ep is further superimposed. When the shape deviation including the probe error is represented by Zd (R1) and Zd (R2), the following formula (16) is used in consideration of the fact that the probe error Ep is constant regardless of the radius of curvature of the surface to be measured. 17) Obtain the equation.
[0067]

[0068]
Α1, β1, γ1 in the equation (16) and α2, β2, γ2 in the equation (17) can be determined by the same estimation calculation as in the above-described conventional example 3. That is, a formula obtained by substituting (X−Xs), (Y−Ys), and (Z−Zs) into X, Y, and Z of the above formula (2 ′) is used as a model formula to minimize the difference from the measured data. Α1, β1, γ1 and α2, β2, γ2 are determined by solving the optimization problem. Since α1 = α + Δα / R1 and α2 = α + Δα / R2, Δα is eliminated from these two equations to obtain the following equation (18). From equation (18), a squareness error α that does not include the effect of the probe error is obtained. Similarly, from the following equations (19) and (20), squareness errors β and γ that do not include the influence of the probe error can be obtained.
[0069]
α = (R1α1-R2α2) / (R1-R2) (18)
β = (R1β1-R2β2) / (R1-R2) (19)
γ = (R1γ1-R2γ2) / (R1-R2) ２ (20)
[0070]
Next, consider a case where R1 is a convex surface and R2 is a concave surface as two reference spheres having different radii of curvature. However, the sign of the radius of curvature is treated as an absolute value without consideration. Since the probe error in the case of measuring the concave surface is rotated by 180 degrees around the Z axis with respect to the case of measuring the convex surface, α2 = α−Δα / R2, and the following equation (18 ′) is obtained. Similarly, from β2 = β−Δβ / R2 and γ2 = γ−Δγ / R2, the following expressions (19 ′) and (20 ′) are obtained.
[0071]
α = (R1α1 + R2α2) / (R1 + R2) (18 ′)
β = (R1β1 + R2β2) / (R1 + R2) (19 ′)
γ = (R1γ1 + R2γ2) / (R1 + R2) (20 ′)
[0072]
As can be seen by comparing the expressions (18), (19), and (20) with the expressions (18 ′), (19 ′), and (20 ′), considering the sign of the radius of curvature, It can be seen that Equations (18), (19) and (20) hold regardless of the irregularities of the reference spherical surface.
[0073]
Further, after determining the squareness errors α, β, and γ from the equations (18), (19), and (20), and substituting them into the equations (16) and (17), the probe error can be obtained. It is also possible to accurately determine Ep. For example, if the equation (16) is used, the probe error Ep can be obtained from the following equation (21).
[0074]

[0075]
The obtained probe error is stored in a storage device as correction data, and can be used for correcting a probe error with respect to measurement data of an arbitrary measurement target.
[0076]
Next, a second embodiment using three reference spheres having different radii of curvature will be described. If three reference spherical surfaces are used, three squareness errors α1, α2 and α3 including the influence of the probe error can be obtained for the true value α of the squareness error to be obtained.
[0077]
α1 = α + Δα / R1 (22)
α2 = α + Δα / R2 (23)
α3 = α + Δα / R3 (24)
[0078]
These equations (22), (23) and (24) can be expressed as the following equation (25).
[0079]
(Equation 4)

[0080]
From this equation (25), α and Δα can be obtained from the following equation (26) using the least squares method.
[0081]
(Equation 5)

[0082]
Here, “−1” represents an inverse matrix, and “T” represents a transposed matrix. β and γ can be similarly obtained. Also, when four or more reference spherical surfaces are used, three squareness errors α, β, and γ can be obtained in the same manner.
[0083]
Further, the squareness error can be obtained by using a plurality of reference measurement objects having similar shapes to each other instead of the reference spherical surface. This is because the probe error becomes constant irrespective of the size of the reference object under the condition that the shapes are similar to each other, and the above-mentioned expressions (16) and (17) are established.
[0084]
Only the method of obtaining α1, β1, γ1 and α2, β2, γ2 is included. In the case of the second embodiment, the squareness error was obtained by approximating the measured data of the reference sphere to an elliptic equation which is a model formula. In the third embodiment described below, the opposite is true. The squareness error is obtained by performing the operation.
[0085]
Since the coordinate transformation matrix Q in equation (1) is a matrix for transforming a spherical surface in an ideal coordinate system into an elliptical surface in a real coordinate system, the inverse matrix Q^{− 1}Is a matrix that converts an ellipsoid into a sphere. Therefore, Q^{− 1}Is performed, and α, β, and γ included in the matrix elements are improved so that the converted data becomes a spherical surface, thereby obtaining a maximum likelihood estimation value of the squareness error. If the shape is known, it goes without saying that the same method can be applied even when the reference measurement object is not a spherical surface.
[0086]
Here, a method of obtaining “shape deviation data” by subtracting an ideal shape from actual measurement data of a reference measurement object and determining three squareness errors using the shape deviation data will be described.
[0087]
First, two ideal convex spherical surfaces having a radius of curvature of R1 and R2 are considered as reference measurement objects. The X, Y, and Z coordinates of each measurement data are divided by the respective radii of curvature to normalize to the measurement data having a radius of curvature of 1 mm. This is because each coordinate data is added or subtracted later, so that it is necessary to adjust the scale as a preparation beforehand. The shape deviation of the normalized data (that is, the shape deviation from the ideal spherical surface of R = 1 mm) is given by the following formulas (16 ') and (17') from formulas (16) and (17).
[0088]

[0089]
Es is obtained by solving the simultaneous equations of the equations (16 ') and (17'). Since Es is a shape deviation caused only by a squareness error in a spherical surface of R = 1 mm, ellipsoidal surface data can be obtained by adding ideal spherical data of R = 1 mm to Es. Then, the squareness errors α, β, γ can be determined by applying the method described in the above embodiment.
[0090]
Next, consider a case where a convex surface having a curvature radius R1 and a concave surface having a curvature radius R2 are used as reference measurement objects. However, the sign of the radius of curvature is treated as an absolute value without consideration. The probe error in the case of the concave surface measurement is as follows in consideration of the fact that the probe is rotated by 180 degrees around the Z axis, the characteristic of the shape distortion, and the expressions (9) to (14) with respect to the case of the convex surface measurement. Equations (16 ") and (17") are obtained.
[0091]

[0092]
Then, the equation (17 ") is rotated by 180 degrees around the Z axis to obtain the following equation (17").
[0093]

[0094]
Es is obtained by solving the simultaneous equations of the equations (16 ″) and (17 ′ ″). Since Es is a shape deviation caused only by a squareness error in a spherical surface of R = 1 mm, Es is R = 1 mm By adding the ideal spherical data, elliptic surface data can be obtained, and the squareness errors α, β, γ can be determined by applying the method described in the first embodiment or the second embodiment.
[0095]
Although the data operation for rotating one of the concave and convex reference spheres by 180 degrees is performed on the shape deviation data in the above description, the reference sphere shape data itself before the shape deviation data is obtained may be rotated.
[0096]
Next, a more generalized case will be described in which three reference measurement objects R1 ', R2', and R3 'which have similar shapes to each other and are not spherical are used. Here, R1 ', R2', and R3 'represent scale factors proportional to the size of each reference object. In this case, the equations corresponding to the equations (16 ') and (17') are expressed as follows.
[0097]

[0098]
Here, the errors Es and Ep caused by the squareness error are represented by Es' and Ep 'with "'" because the profiles are different from the case where the reference measurement object is a spherical surface. The above equations (27), (28) and (29) can be expressed as the following equation (30).
[0099]
(Equation 6)

[0100]
From the equation (30), Es 'and Ep' can be obtained from the following equation (31) using the least squares method.
[0101]
(Equation 7)

[0102]
The squareness errors α, β, and γ are obtained by applying the method described in the first embodiment to the data obtained by adding the ideal shape data with the scale factor R ′ = 1 to Es ′ obtained from the equation (31). Can be determined.
[0103]
In addition, when the concave and convex reference spheres having the same absolute value of the curvature radius are used, the method of obtaining the squareness error described above can be further simplified.
[0104]
Further, the squareness error described in the first embodiment and the second embodiment is obtained by using the equations (18), (19) and (20), but the absolute values of the radii of curvature are equal. When using the concave and convex reference sphere, the simplification becomes as follows: α = (α1 + α2) / 2, β = (β1 + β2) / 2, γ = (γ1 + γ2) / 2.
[0105]
Further, when the concave and convex reference spheres having the same absolute value of the radius of curvature are used in the third embodiment, Es = (Zd (R1) -Zd (R2)^π) / 2.
[0106]
Next, the minimum data required for obtaining the squareness error will be considered. As can be seen from the graph in the center column of FIG. 1, measurement data obtained by passing through the origin (in this case, the vertex of the convex reference sphere or the bottom point of the concave reference sphere is the origin) and parallel to the X axis. Has only sensitivity to the squareness error β. In other words, the squareness error α and the squareness error γ cannot be obtained from the measurement data acquired along the path parallel to the X axis through the origin. Similarly, as can be seen from the graph in the left column of FIG. 1, the measurement data acquired in a path that passes through the origin and is parallel to the Y axis has only a sensitivity to the squareness error α. Therefore, only the squareness error α and the squareness error β can be obtained from the data acquired along the X-axis and the Y-axis in a path parallel to both the origins, and the squareness error γ cannot be determined.
[0107]
Therefore, in order to determine the squareness errors α, β, and γ, it is necessary to acquire measurement data along a measurement path that does not pass through the origin or a path that passes through the origin and is not parallel to the X axis and the Y axis. If two measurement paths are set within an angle range of 45 degrees ± 40 degrees with respect to the X axis and the Y axis through the origin, the squareness errors α, β, and γ can be determined. Furthermore, considering that the shape deviation caused by the squareness errors α and β is only one-fourth of the shape deviation caused by the squareness error γ, it is desirable that the shape deviation be less than 45 degrees with respect to the X axis and the Y axis. It is preferable to acquire the measurement data through two orthogonal paths forming a small angle, for example, about 20 degrees.
[0108]
The squareness error needs to be periodically calibrated, and it is desirable to have an automatic calibration function as one of the functions of the CMM. That is, a function of storing measurement data of two reference spheres having different radii of curvature and automatically calculating a squareness error from the data is provided as one of the functions of the coordinate measuring machine.
[0109]
FIG. 3 is a block diagram showing a configuration of a calibration circuit in the CMM according to the first embodiment of another invention, and FIG. 4 is a flowchart showing an operation of the calibration circuit in the CMM of the embodiment. is there. The operation of the calibration circuit in the coordinate measuring machine of this embodiment will be described with reference to both figures.
[0110]
First, the squareness error initial value setting means 31 of FIG. 3 sets the squareness error initial values, α0, β0, and γ0 (step S101). The initial value is set to a value that is as close to true α, β, and γ as possible in order to shorten the subsequent calculation time and make it difficult to fall into a local optimum solution. For example, the values of the squareness errors α, β, and γ at the time of the previous calibration may be set as the initial values. Then, the reference sphere data is read from the reference sphere data storage means 32 in FIG. 3 in which the reference sphere data is temporarily stored (step S102). Also, the ellipsoid data is generated by the ellipsoid data generation means 33 in FIG. 3 (step S103). Specifically, elliptical surface data is generated from an expression obtained by substituting (X-Xs), (Y-Ys), and (Z-Zs) for X, Y, and Z in the expression (2 '). Next, the difference between the actually measured data of the reference sphere and the ellipsoidal data is calculated by the difference calculation means 34 in FIG. 3, and the square sum of the difference is calculated (step S104). In order to determine whether or not it can be regarded as an optimal solution by the convergence determination means 35 of FIG. 3, for example, the convergence is determined by checking whether the difference between the previously calculated sum of squares and the last calculated sum of squares is sufficiently small. A determination is made (step S105). If the convergence determination is rejected, parameters such as α, β, γ, Xs, Ys, and Zs are improved by the parameter improving means 36 in FIG. 3, and the process returns to step S103 (step S105; NO, step S106). When the convergence is determined, it is determined whether or not a series of arithmetic processing has been completed for the two pieces of reference sphere data (step S105; YES, step S107). If a series of arithmetic processing is not completed, the process returns to step S102 (step S107; NO). If a series of arithmetic processing is completed, the first squareness error obtained from the first reference sphere data and the second squareness error obtained from the second reference sphere data are used, and equation (18) is used. , (19), (20), etc., to calculate the final squareness error value by the squareness error calculating means 37 in FIG. 3 (step S107; YES, step S108). . Next, the numerical value of the squareness error calculated by the probe error calculating means 38 in FIG. 3 is substituted into the equation (16) or (17) to determine the probe error Ep. The information is stored in the storage unit 39 of FIG. 3 (steps S109 and S110).
[0111]
FIG. 5 is a block diagram showing a configuration of a calibration circuit in a CMM according to a second embodiment of another invention, and FIG. 6 is a flowchart showing an operation of the calibration circuit in the CMM of the embodiment. is there. The operation of the calibration circuit in the coordinate measuring machine of this embodiment will be described with reference to both figures.
[0112]
First, the squareness error initial value setting means 51 of FIG. 5 sets the squareness error initial values, α0, β0, and γ0 (step S201). The initial value is set to a value as close as possible to the true squareness errors α, β, and γ as much as possible in order to make the subsequent calculation time shorter and hardly fall into the local optimum solution. For example, the values of the squareness errors α, β, and γ at the time of the previous calibration may be set as the initial values. Then, the reference sphere data is read from the reference sphere data storage means 52 in FIG. 5 in which the reference sphere data is temporarily stored (step S202). Next, with respect to the read reference sphere data, the coordinate transformation means 53 of FIG.^{− 1}(Step S203). Then, the difference between the reference sphere data after the coordinate conversion and the ideal sphere data is calculated by the difference calculation means 54 in FIG. 5, and the square sum of the difference is calculated (step S204). In order to determine whether or not it can be regarded as an optimal solution by the convergence determining means 55 of FIG. 5, for example, the convergence is determined by checking whether the difference between the previously calculated sum of squares and the last calculated sum of squares is sufficiently small. A determination is made (step S205). If the convergence determination is rejected, parameters such as α, β, γ, Xs, Ys, and Zs are improved by the parameter improving means 56 of FIG. 5 and the process returns to step S203 (step S205; NO, step S206). When the convergence is determined, it is determined whether or not a series of arithmetic processing has been completed for the two pieces of reference sphere data (step S205; YES, step S207). If a series of arithmetic processing is not completed, the process returns to step S202 (step S207; NO). If a series of arithmetic processing is completed, the first squareness error obtained from the first reference sphere data and the second squareness error obtained from the second reference sphere data are used, and equation (18) is used. , (19), (20), etc., to calculate the final squareness error value by the squareness error calculating means 57 in FIG. 5 (step S207; YES, step S208). . Next, the numerical value of the squareness error calculated by the probe error calculating means 58 in FIG. 5 is substituted into the equation (16) or (17) to determine the probe error Ep. The information is stored in the storage means 59 of FIG. 5 (steps S209 and S210).
[0113]
FIG. 7 is a block diagram showing a configuration of a calibration circuit in a CMM according to a third embodiment of another invention, and FIG. 8 is a flowchart showing an operation of the calibration circuit in the CMM of the embodiment. is there. The operation of the calibration circuit in the coordinate measuring machine of this embodiment will be described with reference to both figures.
[0114]
First, initial values Xs0, Ys0, Zs0 of the translational amounts of the ideal spherical surface are set by the squareness error initial value setting means 71 in FIG. 7 (step S301). Next, the reference sphere data is read from the reference sphere data storage means 72 of FIG. 7 in which the reference sphere data is stored (step S302). It is determined whether the reference sphere data is a concave surface or a convex surface. If the surface is concave, coordinate conversion is performed by rotating the Z-axis by 180 degrees around the Z axis by the coordinate conversion unit 73 in FIG. 7 (step S303). The convex surface may be rotated without rotating the concave surface. Then, the spherical surface data generating means 74 of FIG. 7 generates ideal spherical surface data translated by Xs, Ys, and Zs in the X, Y, and Z directions, respectively (step S304). The difference between the actually measured data of the reference sphere and the ideal sphere data is calculated by the difference calculation means 75 of FIG. 7, and the square sum of the difference is calculated (step S305). A convergence determination is performed by the convergence determination means 76 in FIG. 7 to determine whether or not the solution can be regarded as an optimal solution (step S306). If the convergence determination is rejected, the parameters of Xs, Ys, and Zs are improved by the parameter improving means 77 of FIG. 7, and the process returns to step S304 (step S306; NO, step S307). If the convergence is determined, it is determined whether a series of arithmetic processing has been completed for the two pieces of reference sphere data (step S308). If a series of arithmetic processing has not been completed, the process returns to step S302 (step S308; NO). If a series of arithmetic processing has been completed, the first shape deviation data obtained from the first reference sphere data and the second shape deviation data obtained from the second reference sphere data are used, and equation (22) is used. The probe error is obtained by the probe error calculation means 79 in FIG. 7 by performing the calculation corresponding to the equation (23) (step S308; YES, step S309). Further, the squareness error calculating means 78 of FIG. 7 calculates a squareness error value by using this (step S310). Finally, information on the obtained squareness error and probe error is stored in the storage means 80 of FIG. 7 (step S311).
[0115]
FIG. 9 is a block diagram showing a configuration of a CMM of another invention. FIG. 10 is a diagram showing a schematic configuration of the coordinate measuring machine of the present invention. As shown in FIG. 9, the coordinate measuring machine includes a three-axis orthogonal stage 91, a shape measuring probe 92, coordinate measuring means 93, a control / calculation unit 94, and an output unit 95. The three-axis orthogonal stage 91 has an X-axis stage 111, a Y-axis stage 112, and a Z-axis stage 113 as shown in FIG. 10C, and a contact-type or non-contact-type shape measurement probe is provided thereon. 92 are attached. An object to be measured is fixed at a position facing the shape measuring probe 92. As shown in FIG. 10, a calibration jig 116 to which reference spheres 114 and 115 having different radii of curvature used for calibration of the measuring machine are fixed is fixed to the coordinate measuring machine via positioning pins 117 and 118. The shape measuring probe 92 scans the surfaces of the reference spherical surfaces 114 and 115 by driving the three-axis orthogonal stage 91 shown in FIG. 9 or operates in a point-to-point manner. The coordinate measuring means 93 in FIG. 9 is not shown in FIG. 10, but is composed of, for example, a laser interferometer. In FIG. The distance from the probe tip (indicated by the dashed arrow in FIG. 10) is sequentially measured with reference to the reference mirrors 119 and 120 installed at an angle. Further, the control / calculation unit 94 in FIG. 9 includes a switching unit 96, a system control unit 97, a calibration data calculation unit 98, and a measurement data correction unit 99. The switching unit 96 switches the output destination of the coordinate data input from the coordinate measuring unit 93 to the calibration data calculation unit 98 or the measurement data correction unit 99 according to the processing mode. As described above, the calibration data calculation unit 98 calculates the squareness error of the coordinate axes (in the case of FIG. 10, three reference mirrors, that is, the reference mirrors) based on the measurement data of the two reference spheres having different radii of curvature. (Corresponding to the squareness between the reference mirrors 119 and 120 and the Z-coordinate measuring reference mirror, not shown), and the probe error is calculated, and the information is stored. The measurement data correction unit 99 corrects the measurement data of the DUT other than the reference sphere using the information on the squareness error and the probe error obtained and stored in the calibration data calculation unit 98. The output unit 95 performs coordinate conversion on the shape data of the DUT for which the squareness error correction and the probe error correction have been performed by the measurement data correction unit 99 to correct a 30-degree tilt component of the laser length measuring optical system. After that, the data is output to a display device or a storage device. Then, the system control unit 97 in FIG. 9 includes storage means for storing the installation positions of the two reference spheres, and automatically measures the shape of the reference sphere based on the installation position information of the reference sphere. The calibration jig 116 to which the reference spheres 114 and 115 shown in FIG. 10 are fixed is positioned by the positioning pins 117 and 118, so that if the installation position of the reference sphere is taught in advance, automatic measurement becomes possible.
[0116]
The reason that the reference mirror for the laser interferometer is arranged at an inclination of 30 degrees is that, as described above, the minimum data necessary for obtaining all the squareness errors is most desirably passed through the origin. It is preferable to acquire the measurement data by two orthogonal paths that form an angle of 30 degrees with respect to the X axis and the Y axis, and the measurement coordinate system of the laser interferometer is changed to a device of the coordinate measuring machine. If the probe is arranged at an angle of 30 degrees with respect to the coordinate system, the probe only needs to be driven in parallel with the XY coordinates from the viewpoint of the three-dimensional measuring machine, and the linear interpolation operation at an oblique angle of 30 degrees can be omitted. Of course, the normal direction of the laser interferometer reference mirror need only be non-parallel to the X-axis and Y-axis of the coordinate measuring machine, and in fact, should be non-parallel within a range of about 45 ± 40 degrees. However, it is not necessarily limited to 30 degrees.
[0117]
Next, FIG. 11 is a block diagram showing a system configuration of the present invention. That is, FIG. 7 shows hardware constructed from a microprocessor or the like that executes software by the method of calibrating the coordinate measuring machine in the above embodiment. In the figure, the calibration system of the CMM includes an interface (hereinafter abbreviated as I / F) 81, a CPU 82, a ROM 83, a RAM 84, a display device 85, a hard disk 86, a keyboard 87, and a CD-ROM drive 88. I have. In addition, a general-purpose processing device is prepared, and a program for executing the calibration method of the CMM of the present invention is stored in a readable storage medium such as the CD-ROM 89. Further, a control signal is input from an external device via the I / F 81, and the keyboard 87 activates an instruction from an operator or automatically activates the program of the present invention. Then, the CPU 82 performs a calibration control process according to the above-described calibration method of the CMM in accordance with the program, stores the processing result in a storage device such as the RAM 84 or the hard disk 86, and outputs the result to the display device 85 or the like as necessary. As described above, by using the medium stored with the program for executing the method for calibrating the CMM of the present invention, it is possible to universally construct a calibration system for the CMM without changing the existing system. Can be.
[0118]
It should be noted that the present invention is not limited to the above embodiment, and it goes without saying that various modifications and substitutions can be made within the scope of the claims.
[0119]
【The invention's effect】
As described above, according to the calibration method of the coordinate measuring machine of the present invention, which has a probe for detecting the position of the surface to be measured in the Z direction, the true surface shape is known, and the shapes are similar to each other. Measuring the shapes of N (N is a positive integer) reference measurement objects and detecting three squareness errors of a three-dimensional orthogonal coordinate axis based on the measured shape data of the N reference measurement objects. There is a feature. Therefore, the influence of the probe error can be eliminated, and the three squareness errors α, β, γ can be obtained with high accuracy even when there is a probe error.
[0120]
Further, for each shape data of the N reference measurement objects, 3 × N squareness errors are obtained by approximating the equation of an ellipse, and three squareness errors are calculated from the 3 × N squareness errors. By detecting, three squareness errors from which the probe error is separated can be obtained.
[0121]
Further, a coordinate conversion matrix that brings the shape data of the reference object closer to the shape of the true reference object is obtained, and 3 × N squareness errors are obtained from matrix elements of the N coordinate conversion matrices. By detecting three squareness errors from the squareness error, the calculation process for determining the squareness error can be further simplified.
[0122]
In addition, by calculating the shape deviation between the shape data of the reference object and the true surface shape, and detecting three squareness errors from the N shape deviation data, the calculation process for obtaining the squareness error is simplified. Can be
[0123]
Further, by performing coordinate conversion for rotating the shape data of the reference measurement object by 180 degrees around the Z axis and by performing coordinate conversion for rotating the shape deviation data by 180 degrees around the Z axis, the squareness error and the probe error can be reduced. Separation becomes possible.
[0124]
Further, it is preferable to use two reference measurement objects or to use reference spheres having different radii of curvature as the reference measurement objects.
[0125]
Further, by using two reference spheres having the same absolute value of the radius of curvature and different signs, the calculation process can be greatly simplified as compared with the case where the absolute values of the radius of curvature are different.
[0126]
When the coordinate measuring directions of the coordinate measuring means of the coordinate measuring machine are X, Y, and Z, at least two lines of measurement data passing through the center of the reference object and being non-parallel to the X and Y directions. Is used to determine the squareness error or the probe error using the minimum necessary data, so that the labor and time for the calibration work can be saved.
[0127]
Further, as another invention, a three-dimensional measuring machine having a probe for detecting a position of a surface to be measured in the Z direction is a N-dimensional measuring machine having a true surface shape known and having similar shapes to each other (N is a positive number). ) For detecting three squareness errors of the three-dimensional orthogonal coordinate axes based on the shape data of the reference object shape data storage unit for storing the shape data of the reference object of the reference object). And an arithmetic unit. Therefore, the influence of the probe error can be eliminated, and even when there is a probe error, the three squareness errors α, β, and γ can be accurately obtained.
[0128]
The calculating unit includes calculating means for calculating a shape deviation between the shape data of the reference measured object and the equation of the ellipse, convergence determining means, improving means for improving the numerical value of the squareness error, and N reference measured objects. Squareness error calculating means for calculating three squareness errors from 3 × N squareness errors obtained by using the shape data of (3). Therefore, the influence of the probe error can be eliminated, and the three squareness errors α, β, γ can be obtained with high accuracy even when there is a probe error.
[0129]
Further, the calculation unit is configured to perform a coordinate conversion for correcting the squareness error on the shape data of the reference object, and an operation for obtaining a shape deviation between the shape data of the reference object after the coordinate conversion and the true surface shape. Means, convergence determining means, improving means for improving the numerical value of the squareness error, and three squareness errors from 3 × N squareness errors obtained using the shape data of the N reference objects. Is calculated. Therefore, the influence of the probe error can be eliminated, and the three squareness errors α, β, γ can be obtained with high accuracy even when there is a probe error.
[0130]
The calculating unit is configured to calculate shape data of the N pieces of reference workpieces and a shape deviation between each of the true surface shapes, and to calculate a squareness error from the N pieces of shape deviation data. Means. Therefore, the influence of the probe error can be eliminated, and the three squareness errors α, β, γ can be obtained with high accuracy even when there is a probe error.
[0131]
Further, by having an arithmetic means for performing coordinate conversion for rotating the shape data of the reference measurement object by 180 degrees about the Z axis, and by having an arithmetic means for performing coordinate conversion for rotating the shape deviation data by 180 degrees about the Z axis, And the squareness error and the probe error can be separated.
[0132]
Further, it is preferable for the coordinate measuring machine to have two reference measurement objects or to have a reference spherical surface having a different radius of curvature as the reference measurement object.
[0133]
Furthermore, by providing two reference spheres having the same absolute value of the radius of curvature and different signs as the reference measurement object, the arithmetic processing can be greatly simplified as compared with the case where the absolute values of the radius of curvature are different.
[0134]
According to another aspect of the present invention, there is provided a computer-readable storage medium storing a program for executing a method of calibrating a coordinate measuring machine having a probe for detecting a position of a surface to be measured in a Z direction by a computer. A function of measuring the shapes of N (N is a positive integer) reference measurement objects whose true surface shapes are known and similar to each other, and based on the measured shape data of the N reference measurement objects. And a program for executing a method of calibrating a three-dimensional measuring machine having a function of detecting three squareness errors of three-dimensional orthogonal coordinate axes. Therefore, the calibration system of the coordinate measuring machine can be universally constructed without changing the existing system.
[0135]
Further, a computer-readable storage medium storing a program for executing a method of calibrating a coordinate measuring machine as another invention has a first data for generating pseudo data from a model formula having a squareness error as a parameter. A function, a second function for calculating a shape deviation between shape data and pseudo data of the reference measurement object, a third function for determining convergence, a fourth function for improving the numerical value of the squareness error, and a convergence determination And a fifth function of repeating the first to fourth functions until the completion of the calculation, and three squareness errors from 3 × N squareness errors obtained for the shape data of the N reference measurement objects. The program for executing the method of calibrating the coordinate measuring machine having the sixth function of calculating the CMM is stored. Therefore, the calibration system of the coordinate measuring machine can be universally constructed without changing the existing system.
[0136]
Further, a computer-readable storage medium storing a program for executing a method of calibrating a coordinate measuring machine as another invention includes a coordinate transformation for correcting a squareness error with respect to shape data of a reference measurement object. A second function of calculating the shape deviation between the shape data of the reference object after coordinate conversion and the shape of the true reference object, a third function of determining convergence, A fourth function for improving the numerical value of the error, a fifth function for repeating the first to fourth functions until the convergence determination is completed, and a third function for the shape data of the N reference measurement objects. A program for executing a method of calibrating a coordinate measuring machine having a sixth function of obtaining three squareness errors from × N squareness errors is stored. Therefore, the calibration system of the coordinate measuring machine can be universally constructed without changing the existing system.
[0137]
Further, a computer-readable storage medium storing a program for executing the calibration method of the coordinate measuring machine as another invention includes a shape deviation between the shape data of the reference object and the shape of the true reference object. A program for executing a method of calibrating a coordinate measuring machine having a first function for calculating and a second function for calculating a squareness error from N shape deviation data is stored. Therefore, the calibration system of the coordinate measuring machine can be universally constructed without changing the existing system.
[0138]
Further, by having a function of performing coordinate conversion for rotating the shape data of the reference measurement object by 180 degrees about the Z axis and a function of performing coordinate conversion for rotating the shape deviation data by 180 degrees about the Z axis, squareness error and A calibration system for a coordinate measuring machine capable of separating a probe error can be universally constructed.
[0139]
Further, by processing the shape data of the two reference measurement objects, a calibration system of the coordinate measuring machine that can separate the squareness error and the probe error can be constructed for general use.
[0140]
Further, it is preferable to process reference sphere data having different radii of curvature.
[0141]
In addition, by processing two reference sphere data having the same absolute value of the radius of curvature and different signs, the operation of the three-dimensional measuring device can be greatly simplified as compared with the case where the absolute value of the radius of curvature is different. A calibration system can be universally constructed.
[Brief description of the drawings]
FIG. 1 is a diagram showing characteristics of a shape deviation for each radius of curvature at a constant squareness error.
FIG. 2 is a characteristic diagram showing a change in shape deviation for each squareness error.
FIG. 3 is a block diagram showing a configuration of a calibration circuit in the coordinate measuring machine according to the first embodiment of another invention.
FIG. 4 is a flowchart illustrating an operation of a calibration circuit in the coordinate measuring machine according to the first embodiment.
FIG. 5 is a block diagram showing a configuration of a calibration circuit in a coordinate measuring machine according to a second embodiment of another invention.
FIG. 6 is a flowchart illustrating an operation of a calibration circuit in the coordinate measuring machine according to the second embodiment.
FIG. 7 is a block diagram showing a configuration of a calibration circuit in a coordinate measuring machine according to a third embodiment of another invention.
FIG. 8 is a flowchart showing the operation of the calibration circuit in the coordinate measuring machine of the third embodiment.
FIG. 9 is a block diagram showing a configuration of a CMM of another invention.
FIG. 10 is a diagram showing a schematic configuration of a coordinate measuring machine according to another invention.
FIG. 11 is a block diagram showing a system configuration of the present invention.
FIG. 12 is a schematic diagram showing a configuration of a contact probe.
FIG. 13 is a schematic diagram showing a configuration of a non-contact probe.
FIG. 14 is a diagram illustrating a coordinate axis squareness error of three axes.
[Explanation of symbols]
31, 51, 71; squareness error initial value setting means, 32, 52, 72; reference sphere data storage means, 33; ellipsoidal data generation means, 34, 54, 75; difference calculation means, 35, 55, 76; Convergence determination means, 36, 56, 77; parameter improvement means, 37, 57, 78; squareness error calculation means, 38, 58, 79; probe error calculation means, 39, 59, 80; storage means, 53, 73; Coordinate conversion means, 74; spherical data generation means, 91; 3-axis orthogonal stage, 92; shape measurement probe, 93; coordinate measurement means, 94; control / calculation section, 95; output section, 96; System control unit, 98; calibration data calculation unit, 99; measurement data correction unit, 100, 200; optical probe.

Claims (28)

In a method of calibrating a coordinate measuring machine having a probe for detecting a position in a Z direction of a surface to be measured,
Measuring the shape of N (N is a positive integer) reference measurement objects whose true surface shapes are known and have similar shapes to each other;
A method for calibrating a three-dimensional measuring machine, comprising detecting three squareness errors of a three-dimensional orthogonal coordinate axis based on measured shape data of N reference measurement objects. For each of the shape data of the N reference measurement objects, 3 × N squareness errors are obtained by approximating an elliptic equation, and three squareness errors are detected from the 3 × N squareness errors. The method for calibrating a coordinate measuring machine according to claim 1. A coordinate conversion matrix for bringing the shape data of the reference object closer to the shape of the true reference object is obtained, and 3 × N squareness errors are obtained from matrix elements of the N coordinate conversion matrices. 2. The method for calibrating a coordinate measuring machine according to claim 1, wherein three squareness errors are detected from the angle errors. 2. The method according to claim 1, wherein a shape deviation between the shape data of the reference object and the true surface shape is calculated, and three squareness errors are detected from the N shape deviation data. 5. The calibration method for a coordinate measuring machine according to claim 4, wherein coordinate transformation is performed to rotate the shape data of the reference measurement object by 180 degrees around the Z axis. 5. The method for calibrating a coordinate measuring machine according to claim 4, wherein coordinate transformation for rotating the shape deviation data by 180 degrees around the Z axis is performed. The method for calibrating a coordinate measuring machine according to claim 1, wherein two reference objects are used. The method for calibrating a coordinate measuring machine according to any one of claims 1 to 7, wherein a reference sphere having a different radius of curvature is used as the reference measurement object. 9. The method for calibrating a coordinate measuring machine according to claim 1, wherein two reference spheres having the same absolute value of curvature radius and different signs are used. When the coordinate measuring directions of the coordinate measuring means of the coordinate measuring machine are X, Y, and Z, at least two lines of measurement data that pass through the center of the reference measurement object and are non-parallel to the X direction and the Y direction are obtained. A method for calibrating a coordinate measuring machine according to any one of claims 1 to 9, which is used. In a coordinate measuring machine having a probe for detecting the position of the surface to be measured in the Z direction,
A reference measurement object shape data storage unit that stores shape data of N (N is a positive integer) reference measurement objects whose true surface shapes are known and have similar shapes to each other;
A three-dimensional measuring machine comprising: a calculation unit for detecting three squareness errors of a three-dimensional orthogonal coordinate axis based on shape data of N reference objects. The calculating unit includes calculating means for calculating a shape deviation between the shape data of the reference measurement object and an elliptic equation, convergence determining means, improving means for improving a numerical value of squareness error, and N pieces of the reference measurement 12. The three-dimensional measuring machine according to claim 11, further comprising a squareness error calculating means for calculating three squareness errors from 3 × N squareness errors obtained using the shape data of the object. The computing unit is configured to perform a coordinate transformation for correcting a squareness error on the shape data of the reference object, and obtain a shape deviation between the shape data of the reference object after the coordinate transformation and a true surface shape. Calculating means, convergence determining means, improving means for improving the numerical value of the squareness error, and three squareness angles from 3 × N squareness errors obtained using the shape data of the N reference objects. 12. The coordinate measuring machine according to claim 11, further comprising a squareness error calculating means for calculating an error. The calculating unit is configured to calculate a shape deviation between the shape data of the N reference measurement objects and the true surface shape thereof, and a squareness error calculation for calculating a squareness error from the N shape deviation data. The coordinate measuring machine according to claim 11, comprising means. The coordinate measuring machine according to claim 14, further comprising a calculation unit that performs coordinate conversion for rotating the shape data of the reference measurement object by 180 degrees about the Z axis. The coordinate measuring machine according to claim 14, further comprising a calculation unit that performs coordinate conversion for rotating the shape deviation data by 180 degrees about the Z axis. The coordinate measuring machine according to any one of claims 11 to 16, comprising two reference measurement objects. The coordinate measuring machine according to any one of claims 11 to 17, further comprising a reference spherical surface having a different radius of curvature as the reference measurement object. The coordinate measuring machine according to any one of claims 11 to 18, comprising two reference spherical surfaces having the same absolute value of the radius of curvature and different signs as the reference measurement object. By a computer, in a computer-readable storage medium storing a program for executing a calibration method of a coordinate measuring machine having a probe for detecting a position of a surface to be measured in a Z direction,
A function of measuring the shapes of N (N is a positive integer) reference measurement objects whose true surface shapes are known and have similar shapes to each other;
A computer storing a program for executing a calibration method of a three-dimensional measuring machine having a function of detecting three squareness errors of three-dimensional orthogonal coordinate axes based on measured shape data of N reference measurement objects. A readable storage medium. The computer processes shape data of N (N is a positive integer) reference measurement objects, and executes a calibration method of the CMM having a probe for detecting a position in the Z direction of the surface to be measured. Computer-readable storage medium storing a program for
A first function of generating pseudo data from a model equation having a squareness error as a parameter,
A second function of calculating a shape deviation between the shape data of the reference object and the pseudo data;
A third function for determining convergence;
A fourth function for improving the numerical value of the squareness error,
A fifth function of repeating the first to fourth functions until the convergence determination is completed;
A sixth function of calculating three squareness errors from 3 × N squareness errors obtained with respect to the shape data of the N reference measurement objects, and a sixth function of executing the calibration method of the coordinate measuring machine. A computer-readable storage medium storing a program. The computer processes shape data of N (N is a positive integer) reference measurement objects, and executes a calibration method of the CMM having a probe for detecting a position in the Z direction of the surface to be measured. Computer-readable storage medium storing a program for
A first function of performing coordinate transformation on the shape data of the reference measurement object to correct a squareness error;
A second function of calculating a shape deviation between the shape data of the reference object after the coordinate transformation and the shape of the true reference object;
A third function for determining convergence;
A fourth function for improving the numerical value of the squareness error,
A fifth function of repeating the first to fourth functions until the convergence determination is completed;
And a sixth function for obtaining three squareness errors from 3 × N squareness errors obtained for the shape data of the N reference measurement objects. A computer-readable storage medium storing a program. The computer processes shape data of N (N is a positive integer) reference measurement objects, and executes a calibration method of the CMM having a probe for detecting a position in the Z direction of the surface to be measured. Computer-readable storage medium storing a program for
A first function of calculating a shape deviation between the shape data of the reference object and the shape of the true reference object;
A computer-readable storage medium storing a program for executing a calibration method of a CMM having a second function of calculating a squareness error from N pieces of shape deviation data. 24. A computer-readable storage storing a program for executing a method of calibrating a coordinate measuring machine according to claim 23, further comprising a function of performing coordinate conversion for rotating the shape data of the reference measurement object by 180 degrees around the Z axis. Medium. 24. A computer-readable storage medium storing a program for executing a method for calibrating a coordinate measuring machine according to claim 23, having a function of performing coordinate conversion for rotating shape deviation data by 180 degrees around a Z-axis. 26. A computer-readable storage medium storing a program for executing the method of calibrating a coordinate measuring machine according to claim 20, wherein the computer executes processing of shape data of two reference objects. 27. A computer-readable storage medium storing a program for executing the method for calibrating a coordinate measuring machine according to claim 20, which processes reference sphere data having different radii of curvature. 28. A computer readable program storing a program for executing the method for calibrating a coordinate measuring machine according to claim 20, wherein two reference sphere data having the same absolute value of curvature radius and different signs are processed. Storage media.

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